1,1,51,57,0.0882998,"\int x^5 \left(a+b \sin \left(c+d x^2\right)\right) \, dx","Integrate[x^5*(a + b*Sin[c + d*x^2]),x]","\frac{a d^3 x^6-3 b \left(d^2 x^4-2\right) \cos \left(c+d x^2\right)+6 b d x^2 \sin \left(c+d x^2\right)}{6 d^3}","\frac{a x^6}{6}+\frac{b \cos \left(c+d x^2\right)}{d^3}+\frac{b x^2 \sin \left(c+d x^2\right)}{d^2}-\frac{b x^4 \cos \left(c+d x^2\right)}{2 d}",1,"(a*d^3*x^6 - 3*b*(-2 + d^2*x^4)*Cos[c + d*x^2] + 6*b*d*x^2*Sin[c + d*x^2])/(6*d^3)","A",1
2,1,44,44,0.0048209,"\int x^3 \left(a+b \sin \left(c+d x^2\right)\right) \, dx","Integrate[x^3*(a + b*Sin[c + d*x^2]),x]","\frac{a x^4}{4}+\frac{b \sin \left(c+d x^2\right)}{2 d^2}-\frac{b x^2 \cos \left(c+d x^2\right)}{2 d}","\frac{a x^4}{4}+\frac{b \sin \left(c+d x^2\right)}{2 d^2}-\frac{b x^2 \cos \left(c+d x^2\right)}{2 d}",1,"(a*x^4)/4 - (b*x^2*Cos[c + d*x^2])/(2*d) + (b*Sin[c + d*x^2])/(2*d^2)","A",1
3,1,41,25,0.0131993,"\int x \left(a+b \sin \left(c+d x^2\right)\right) \, dx","Integrate[x*(a + b*Sin[c + d*x^2]),x]","\frac{a x^2}{2}+\frac{b \sin (c) \sin \left(d x^2\right)}{2 d}-\frac{b \cos (c) \cos \left(d x^2\right)}{2 d}","\frac{a x^2}{2}-\frac{b \cos \left(c+d x^2\right)}{2 d}",1,"(a*x^2)/2 - (b*Cos[c]*Cos[d*x^2])/(2*d) + (b*Sin[c]*Sin[d*x^2])/(2*d)","A",1
4,1,29,31,0.0468892,"\int \frac{a+b \sin \left(c+d x^2\right)}{x} \, dx","Integrate[(a + b*Sin[c + d*x^2])/x,x]","a \log (x)+\frac{1}{2} b \left(\sin (c) \text{Ci}\left(d x^2\right)+\cos (c) \text{Si}\left(d x^2\right)\right)","a \log (x)+\frac{1}{2} b \sin (c) \text{Ci}\left(d x^2\right)+\frac{1}{2} b \cos (c) \text{Si}\left(d x^2\right)",1,"a*Log[x] + (b*(CosIntegral[d*x^2]*Sin[c] + Cos[c]*SinIntegral[d*x^2]))/2","A",1
5,1,48,53,0.0811863,"\int \frac{a+b \sin \left(c+d x^2\right)}{x^3} \, dx","Integrate[(a + b*Sin[c + d*x^2])/x^3,x]","-\frac{a-b d x^2 \cos (c) \text{Ci}\left(d x^2\right)+b d x^2 \sin (c) \text{Si}\left(d x^2\right)+b \sin \left(c+d x^2\right)}{2 x^2}","-\frac{a}{2 x^2}+\frac{1}{2} b d \cos (c) \text{Ci}\left(d x^2\right)-\frac{1}{2} b d \sin (c) \text{Si}\left(d x^2\right)-\frac{b \sin \left(c+d x^2\right)}{2 x^2}",1,"-1/2*(a - b*d*x^2*Cos[c]*CosIntegral[d*x^2] + b*Sin[c + d*x^2] + b*d*x^2*Sin[c]*SinIntegral[d*x^2])/x^2","A",1
6,1,86,74,0.091822,"\int \frac{a+b \sin \left(c+d x^2\right)}{x^5} \, dx","Integrate[(a + b*Sin[c + d*x^2])/x^5,x]","-\frac{a}{4 x^4}-\frac{1}{4} b d^2 \left(\sin (c) \text{Ci}\left(d x^2\right)+\cos (c) \text{Si}\left(d x^2\right)\right)-\frac{b \cos \left(d x^2\right) \left(d x^2 \cos (c)+\sin (c)\right)}{4 x^4}+\frac{b \sin \left(d x^2\right) \left(d x^2 \sin (c)-\cos (c)\right)}{4 x^4}","-\frac{a}{4 x^4}-\frac{1}{4} b d^2 \sin (c) \text{Ci}\left(d x^2\right)-\frac{1}{4} b d^2 \cos (c) \text{Si}\left(d x^2\right)-\frac{b d \cos \left(c+d x^2\right)}{4 x^2}-\frac{b \sin \left(c+d x^2\right)}{4 x^4}",1,"-1/4*a/x^4 - (b*Cos[d*x^2]*(d*x^2*Cos[c] + Sin[c]))/(4*x^4) + (b*(-Cos[c] + d*x^2*Sin[c])*Sin[d*x^2])/(4*x^4) - (b*d^2*(CosIntegral[d*x^2]*Sin[c] + Cos[c]*SinIntegral[d*x^2]))/4","A",1
7,1,125,121,0.255318,"\int x^4 \left(a+b \sin \left(c+d x^2\right)\right) \, dx","Integrate[x^4*(a + b*Sin[c + d*x^2]),x]","\frac{a x^5}{5}-\frac{3 \sqrt{\frac{\pi }{2}} b \left(\sin (c) C\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)+\cos (c) S\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)\right)}{4 d^{5/2}}-\frac{b x \cos \left(d x^2\right) \left(2 d x^2 \cos (c)-3 \sin (c)\right)}{4 d^2}+\frac{b x \sin \left(d x^2\right) \left(2 d x^2 \sin (c)+3 \cos (c)\right)}{4 d^2}","\frac{a x^5}{5}-\frac{3 \sqrt{\frac{\pi }{2}} b \sin (c) C\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)}{4 d^{5/2}}-\frac{3 \sqrt{\frac{\pi }{2}} b \cos (c) S\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)}{4 d^{5/2}}+\frac{3 b x \sin \left(c+d x^2\right)}{4 d^2}-\frac{b x^3 \cos \left(c+d x^2\right)}{2 d}",1,"(a*x^5)/5 - (b*x*Cos[d*x^2]*(2*d*x^2*Cos[c] - 3*Sin[c]))/(4*d^2) - (3*b*Sqrt[Pi/2]*(Cos[c]*FresnelS[Sqrt[d]*Sqrt[2/Pi]*x] + FresnelC[Sqrt[d]*Sqrt[2/Pi]*x]*Sin[c]))/(4*d^(5/2)) + (b*x*(3*Cos[c] + 2*d*x^2*Sin[c])*Sin[d*x^2])/(4*d^2)","A",1
8,1,104,102,0.1964727,"\int x^2 \left(a+b \sin \left(c+d x^2\right)\right) \, dx","Integrate[x^2*(a + b*Sin[c + d*x^2]),x]","\frac{a x^3}{3}+\frac{\sqrt{\frac{\pi }{2}} b \left(\cos (c) C\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)-\sin (c) S\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)\right)}{2 d^{3/2}}+\frac{b x \sin (c) \sin \left(d x^2\right)}{2 d}-\frac{b x \cos (c) \cos \left(d x^2\right)}{2 d}","\frac{a x^3}{3}+\frac{\sqrt{\frac{\pi }{2}} b \cos (c) C\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)}{2 d^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} b \sin (c) S\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)}{2 d^{3/2}}-\frac{b x \cos \left(c+d x^2\right)}{2 d}",1,"(a*x^3)/3 - (b*x*Cos[c]*Cos[d*x^2])/(2*d) + (b*Sqrt[Pi/2]*(Cos[c]*FresnelC[Sqrt[d]*Sqrt[2/Pi]*x] - FresnelS[Sqrt[d]*Sqrt[2/Pi]*x]*Sin[c]))/(2*d^(3/2)) + (b*x*Sin[c]*Sin[d*x^2])/(2*d)","A",1
9,1,61,74,0.1477127,"\int \left(a+b \sin \left(c+d x^2\right)\right) \, dx","Integrate[a + b*Sin[c + d*x^2],x]","a x+\frac{\sqrt{\frac{\pi }{2}} b \left(\sin (c) C\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)+\cos (c) S\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)\right)}{\sqrt{d}}","a x+\frac{\sqrt{\frac{\pi }{2}} b \sin (c) C\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)}{\sqrt{d}}+\frac{\sqrt{\frac{\pi }{2}} b \cos (c) S\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)}{\sqrt{d}}",1,"a*x + (b*Sqrt[Pi/2]*(Cos[c]*FresnelS[Sqrt[d]*Sqrt[2/Pi]*x] + FresnelC[Sqrt[d]*Sqrt[2/Pi]*x]*Sin[c]))/Sqrt[d]","A",1
10,1,91,88,0.188634,"\int \frac{a+b \sin \left(c+d x^2\right)}{x^2} \, dx","Integrate[(a + b*Sin[c + d*x^2])/x^2,x]","-\frac{a}{x}+\sqrt{2 \pi } b \sqrt{d} \left(\cos (c) C\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)-\sin (c) S\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)\right)-\frac{b \sin (c) \cos \left(d x^2\right)}{x}-\frac{b \cos (c) \sin \left(d x^2\right)}{x}","-\frac{a}{x}+\sqrt{2 \pi } b \sqrt{d} \cos (c) C\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)-\sqrt{2 \pi } b \sqrt{d} \sin (c) S\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)-\frac{b \sin \left(c+d x^2\right)}{x}",1,"-(a/x) - (b*Cos[d*x^2]*Sin[c])/x + b*Sqrt[d]*Sqrt[2*Pi]*(Cos[c]*FresnelC[Sqrt[d]*Sqrt[2/Pi]*x] - FresnelS[Sqrt[d]*Sqrt[2/Pi]*x]*Sin[c]) - (b*Cos[c]*Sin[d*x^2])/x","A",1
11,1,119,114,0.2268148,"\int \frac{a+b \sin \left(c+d x^2\right)}{x^4} \, dx","Integrate[(a + b*Sin[c + d*x^2])/x^4,x]","-\frac{a}{3 x^3}-\frac{2}{3} \sqrt{2 \pi } b d^{3/2} \left(\sin (c) C\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)+\cos (c) S\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)\right)-\frac{b \cos \left(d x^2\right) \left(2 d x^2 \cos (c)+\sin (c)\right)}{3 x^3}+\frac{b \sin \left(d x^2\right) \left(2 d x^2 \sin (c)-\cos (c)\right)}{3 x^3}","-\frac{a}{3 x^3}-\frac{2}{3} \sqrt{2 \pi } b d^{3/2} \sin (c) C\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)-\frac{2}{3} \sqrt{2 \pi } b d^{3/2} \cos (c) S\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)-\frac{2 b d \cos \left(c+d x^2\right)}{3 x}-\frac{b \sin \left(c+d x^2\right)}{3 x^3}",1,"-1/3*a/x^3 - (b*Cos[d*x^2]*(2*d*x^2*Cos[c] + Sin[c]))/(3*x^3) - (2*b*d^(3/2)*Sqrt[2*Pi]*(Cos[c]*FresnelS[Sqrt[d]*Sqrt[2/Pi]*x] + FresnelC[Sqrt[d]*Sqrt[2/Pi]*x]*Sin[c]))/3 + (b*(-Cos[c] + 2*d*x^2*Sin[c])*Sin[d*x^2])/(3*x^3)","A",1
12,1,122,163,0.3937449,"\int x^5 \left(a+b \sin \left(c+d x^2\right)\right)^2 \, dx","Integrate[x^5*(a + b*Sin[c + d*x^2])^2,x]","\frac{8 a^2 d^3 x^6-48 a b \left(d^2 x^4-2\right) \cos \left(c+d x^2\right)+96 a b d x^2 \sin \left(c+d x^2\right)-6 b^2 d^2 x^4 \sin \left(2 \left(c+d x^2\right)\right)+3 b^2 \sin \left(2 \left(c+d x^2\right)\right)-6 b^2 d x^2 \cos \left(2 \left(c+d x^2\right)\right)+4 b^2 d^3 x^6}{48 d^3}","\frac{a^2 x^6}{6}+\frac{2 a b \cos \left(c+d x^2\right)}{d^3}+\frac{2 a b x^2 \sin \left(c+d x^2\right)}{d^2}-\frac{a b x^4 \cos \left(c+d x^2\right)}{d}+\frac{b^2 \sin \left(c+d x^2\right) \cos \left(c+d x^2\right)}{8 d^3}+\frac{b^2 x^2 \sin ^2\left(c+d x^2\right)}{4 d^2}-\frac{b^2 x^4 \sin \left(c+d x^2\right) \cos \left(c+d x^2\right)}{4 d}-\frac{b^2 x^2}{8 d^2}+\frac{b^2 x^6}{12}",1,"(8*a^2*d^3*x^6 + 4*b^2*d^3*x^6 - 48*a*b*(-2 + d^2*x^4)*Cos[c + d*x^2] - 6*b^2*d*x^2*Cos[2*(c + d*x^2)] + 96*a*b*d*x^2*Sin[c + d*x^2] + 3*b^2*Sin[2*(c + d*x^2)] - 6*b^2*d^2*x^4*Sin[2*(c + d*x^2)])/(48*d^3)","A",1
13,1,92,102,0.2303229,"\int x^3 \left(a+b \sin \left(c+d x^2\right)\right)^2 \, dx","Integrate[x^3*(a + b*Sin[c + d*x^2])^2,x]","\frac{4 a^2 d^2 x^4+16 a b \sin \left(c+d x^2\right)-16 a b d x^2 \cos \left(c+d x^2\right)-2 b^2 d x^2 \sin \left(2 \left(c+d x^2\right)\right)-b^2 \cos \left(2 \left(c+d x^2\right)\right)+2 b^2 d^2 x^4}{16 d^2}","\frac{a^2 x^4}{4}+\frac{a b \sin \left(c+d x^2\right)}{d^2}-\frac{a b x^2 \cos \left(c+d x^2\right)}{d}+\frac{b^2 \sin ^2\left(c+d x^2\right)}{8 d^2}-\frac{b^2 x^2 \sin \left(c+d x^2\right) \cos \left(c+d x^2\right)}{4 d}+\frac{b^2 x^4}{8}",1,"(4*a^2*d^2*x^4 + 2*b^2*d^2*x^4 - 16*a*b*d*x^2*Cos[c + d*x^2] - b^2*Cos[2*(c + d*x^2)] + 16*a*b*Sin[c + d*x^2] - 2*b^2*d*x^2*Sin[2*(c + d*x^2)])/(16*d^2)","A",1
14,1,52,58,0.1281868,"\int x \left(a+b \sin \left(c+d x^2\right)\right)^2 \, dx","Integrate[x*(a + b*Sin[c + d*x^2])^2,x]","-\frac{-2 \left(2 a^2+b^2\right) \left(c+d x^2\right)+8 a b \cos \left(c+d x^2\right)+b^2 \sin \left(2 \left(c+d x^2\right)\right)}{8 d}","\frac{1}{4} x^2 \left(2 a^2+b^2\right)-\frac{a b \cos \left(c+d x^2\right)}{d}-\frac{b^2 \sin \left(c+d x^2\right) \cos \left(c+d x^2\right)}{4 d}",1,"-1/8*(-2*(2*a^2 + b^2)*(c + d*x^2) + 8*a*b*Cos[c + d*x^2] + b^2*Sin[2*(c + d*x^2)])/d","A",1
15,1,71,74,0.1659129,"\int \frac{\left(a+b \sin \left(c+d x^2\right)\right)^2}{x} \, dx","Integrate[(a + b*Sin[c + d*x^2])^2/x,x]","\frac{1}{2} \left(2 a^2+b^2\right) \log (x)-\frac{1}{4} b \left(-4 a \sin (c) \text{Ci}\left(d x^2\right)-4 a \cos (c) \text{Si}\left(d x^2\right)+b \cos (2 c) \text{Ci}\left(2 d x^2\right)-b \sin (2 c) \text{Si}\left(2 d x^2\right)\right)","\frac{1}{2} \left(2 a^2+b^2\right) \log (x)+a b \sin (c) \text{Ci}\left(d x^2\right)+a b \cos (c) \text{Si}\left(d x^2\right)-\frac{1}{4} b^2 \cos (2 c) \text{Ci}\left(2 d x^2\right)+\frac{1}{4} b^2 \sin (2 c) \text{Si}\left(2 d x^2\right)",1,"((2*a^2 + b^2)*Log[x])/2 - (b*(b*Cos[2*c]*CosIntegral[2*d*x^2] - 4*a*CosIntegral[d*x^2]*Sin[c] - 4*a*Cos[c]*SinIntegral[d*x^2] - b*Sin[2*c]*SinIntegral[2*d*x^2]))/4","A",1
16,1,116,115,0.2594078,"\int \frac{\left(a+b \sin \left(c+d x^2\right)\right)^2}{x^3} \, dx","Integrate[(a + b*Sin[c + d*x^2])^2/x^3,x]","\frac{-2 a^2+4 a b d x^2 \cos (c) \text{Ci}\left(d x^2\right)-4 a b d x^2 \sin (c) \text{Si}\left(d x^2\right)-4 a b \sin \left(c+d x^2\right)+2 b^2 d x^2 \sin (2 c) \text{Ci}\left(2 d x^2\right)+2 b^2 d x^2 \cos (2 c) \text{Si}\left(2 d x^2\right)+b^2 \cos \left(2 \left(c+d x^2\right)\right)-b^2}{4 x^2}","-\frac{2 a^2+b^2}{4 x^2}+a b d \cos (c) \text{Ci}\left(d x^2\right)-a b d \sin (c) \text{Si}\left(d x^2\right)-\frac{a b \sin \left(c+d x^2\right)}{x^2}+\frac{1}{2} b^2 d \sin (2 c) \text{Ci}\left(2 d x^2\right)+\frac{1}{2} b^2 d \cos (2 c) \text{Si}\left(2 d x^2\right)+\frac{b^2 \cos \left(2 \left(c+d x^2\right)\right)}{4 x^2}",1,"(-2*a^2 - b^2 + b^2*Cos[2*(c + d*x^2)] + 4*a*b*d*x^2*Cos[c]*CosIntegral[d*x^2] + 2*b^2*d*x^2*CosIntegral[2*d*x^2]*Sin[2*c] - 4*a*b*Sin[c + d*x^2] - 4*a*b*d*x^2*Sin[c]*SinIntegral[d*x^2] + 2*b^2*d*x^2*Cos[2*c]*SinIntegral[2*d*x^2])/(4*x^2)","A",1
17,1,158,169,0.4676695,"\int \frac{\left(a+b \sin \left(c+d x^2\right)\right)^2}{x^5} \, dx","Integrate[(a + b*Sin[c + d*x^2])^2/x^5,x]","-\frac{2 a^2+4 a b d^2 x^4 \sin (c) \text{Ci}\left(d x^2\right)+4 a b d^2 x^4 \cos (c) \text{Si}\left(d x^2\right)+4 a b \sin \left(c+d x^2\right)+4 a b d x^2 \cos \left(c+d x^2\right)-4 b^2 d^2 x^4 \cos (2 c) \text{Ci}\left(2 d x^2\right)+4 b^2 d^2 x^4 \sin (2 c) \text{Si}\left(2 d x^2\right)+2 b^2 d x^2 \sin \left(2 \left(c+d x^2\right)\right)-b^2 \cos \left(2 \left(c+d x^2\right)\right)+b^2}{8 x^4}","-\frac{2 a^2+b^2}{8 x^4}-\frac{1}{2} a b d^2 \sin (c) \text{Ci}\left(d x^2\right)-\frac{1}{2} a b d^2 \cos (c) \text{Si}\left(d x^2\right)-\frac{a b d \cos \left(c+d x^2\right)}{2 x^2}-\frac{a b \sin \left(c+d x^2\right)}{2 x^4}+\frac{1}{2} b^2 d^2 \cos (2 c) \text{Ci}\left(2 d x^2\right)-\frac{1}{2} b^2 d^2 \sin (2 c) \text{Si}\left(2 d x^2\right)-\frac{b^2 d \sin \left(2 \left(c+d x^2\right)\right)}{4 x^2}+\frac{b^2 \cos \left(2 \left(c+d x^2\right)\right)}{8 x^4}",1,"-1/8*(2*a^2 + b^2 + 4*a*b*d*x^2*Cos[c + d*x^2] - b^2*Cos[2*(c + d*x^2)] - 4*b^2*d^2*x^4*Cos[2*c]*CosIntegral[2*d*x^2] + 4*a*b*d^2*x^4*CosIntegral[d*x^2]*Sin[c] + 4*a*b*Sin[c + d*x^2] + 2*b^2*d*x^2*Sin[2*(c + d*x^2)] + 4*a*b*d^2*x^4*Cos[c]*SinIntegral[d*x^2] + 4*b^2*d^2*x^4*Sin[2*c]*SinIntegral[2*d*x^2])/x^4","A",1
18,1,234,247,0.5904911,"\int x^4 \left(a+b \sin \left(c+d x^2\right)\right)^2 \, dx","Integrate[x^4*(a + b*Sin[c + d*x^2])^2,x]","\frac{64 a^2 d^{5/2} x^5-320 a b d^{3/2} x^3 \cos \left(c+d x^2\right)-240 \sqrt{2 \pi } a b \sin (c) C\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)-240 \sqrt{2 \pi } a b \cos (c) S\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)+480 a b \sqrt{d} x \sin \left(c+d x^2\right)-40 b^2 d^{3/2} x^3 \sin \left(2 \left(c+d x^2\right)\right)+15 \sqrt{\pi } b^2 \cos (2 c) C\left(\frac{2 \sqrt{d} x}{\sqrt{\pi }}\right)-15 \sqrt{\pi } b^2 \sin (2 c) S\left(\frac{2 \sqrt{d} x}{\sqrt{\pi }}\right)-30 b^2 \sqrt{d} x \cos \left(2 \left(c+d x^2\right)\right)+32 b^2 d^{5/2} x^5}{320 d^{5/2}}","\frac{1}{10} x^5 \left(2 a^2+b^2\right)-\frac{3 \sqrt{\frac{\pi }{2}} a b \sin (c) C\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)}{2 d^{5/2}}-\frac{3 \sqrt{\frac{\pi }{2}} a b \cos (c) S\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)}{2 d^{5/2}}+\frac{3 a b x \sin \left(c+d x^2\right)}{2 d^2}-\frac{a b x^3 \cos \left(c+d x^2\right)}{d}+\frac{3 \sqrt{\pi } b^2 \cos (2 c) C\left(\frac{2 \sqrt{d} x}{\sqrt{\pi }}\right)}{64 d^{5/2}}-\frac{3 \sqrt{\pi } b^2 \sin (2 c) S\left(\frac{2 \sqrt{d} x}{\sqrt{\pi }}\right)}{64 d^{5/2}}-\frac{3 b^2 x \cos \left(2 c+2 d x^2\right)}{32 d^2}-\frac{b^2 x^3 \sin \left(2 c+2 d x^2\right)}{8 d}",1,"(64*a^2*d^(5/2)*x^5 + 32*b^2*d^(5/2)*x^5 - 320*a*b*d^(3/2)*x^3*Cos[c + d*x^2] - 30*b^2*Sqrt[d]*x*Cos[2*(c + d*x^2)] + 15*b^2*Sqrt[Pi]*Cos[2*c]*FresnelC[(2*Sqrt[d]*x)/Sqrt[Pi]] - 240*a*b*Sqrt[2*Pi]*Cos[c]*FresnelS[Sqrt[d]*Sqrt[2/Pi]*x] - 240*a*b*Sqrt[2*Pi]*FresnelC[Sqrt[d]*Sqrt[2/Pi]*x]*Sin[c] - 15*b^2*Sqrt[Pi]*FresnelS[(2*Sqrt[d]*x)/Sqrt[Pi]]*Sin[2*c] + 480*a*b*Sqrt[d]*x*Sin[c + d*x^2] - 40*b^2*d^(3/2)*x^3*Sin[2*(c + d*x^2)])/(320*d^(5/2))","A",1
19,1,191,198,0.5437614,"\int x^2 \left(a+b \sin \left(c+d x^2\right)\right)^2 \, dx","Integrate[x^2*(a + b*Sin[c + d*x^2])^2,x]","\frac{16 a^2 d^{3/2} x^3+24 \sqrt{2 \pi } a b \cos (c) C\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)-24 \sqrt{2 \pi } a b \sin (c) S\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)-48 a b \sqrt{d} x \cos \left(c+d x^2\right)+3 \sqrt{\pi } b^2 \sin (2 c) C\left(\frac{2 \sqrt{d} x}{\sqrt{\pi }}\right)+3 \sqrt{\pi } b^2 \cos (2 c) S\left(\frac{2 \sqrt{d} x}{\sqrt{\pi }}\right)-6 b^2 \sqrt{d} x \sin \left(2 \left(c+d x^2\right)\right)+8 b^2 d^{3/2} x^3}{48 d^{3/2}}","\frac{1}{6} x^3 \left(2 a^2+b^2\right)+\frac{\sqrt{\frac{\pi }{2}} a b \cos (c) C\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)}{d^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} a b \sin (c) S\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)}{d^{3/2}}-\frac{a b x \cos \left(c+d x^2\right)}{d}+\frac{\sqrt{\pi } b^2 \sin (2 c) C\left(\frac{2 \sqrt{d} x}{\sqrt{\pi }}\right)}{16 d^{3/2}}+\frac{\sqrt{\pi } b^2 \cos (2 c) S\left(\frac{2 \sqrt{d} x}{\sqrt{\pi }}\right)}{16 d^{3/2}}-\frac{b^2 x \sin \left(2 c+2 d x^2\right)}{8 d}",1,"(16*a^2*d^(3/2)*x^3 + 8*b^2*d^(3/2)*x^3 - 48*a*b*Sqrt[d]*x*Cos[c + d*x^2] + 24*a*b*Sqrt[2*Pi]*Cos[c]*FresnelC[Sqrt[d]*Sqrt[2/Pi]*x] + 3*b^2*Sqrt[Pi]*Cos[2*c]*FresnelS[(2*Sqrt[d]*x)/Sqrt[Pi]] - 24*a*b*Sqrt[2*Pi]*FresnelS[Sqrt[d]*Sqrt[2/Pi]*x]*Sin[c] + 3*b^2*Sqrt[Pi]*FresnelC[(2*Sqrt[d]*x)/Sqrt[Pi]]*Sin[2*c] - 6*b^2*Sqrt[d]*x*Sin[2*(c + d*x^2)])/(48*d^(3/2))","A",1
20,1,147,153,0.3279037,"\int \left(a+b \sin \left(c+d x^2\right)\right)^2 \, dx","Integrate[(a + b*Sin[c + d*x^2])^2,x]","\frac{4 a^2 \sqrt{d} x+4 \sqrt{2 \pi } a b \sin (c) C\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)+4 \sqrt{2 \pi } a b \cos (c) S\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)-\sqrt{\pi } b^2 \cos (2 c) C\left(\frac{2 \sqrt{d} x}{\sqrt{\pi }}\right)+\sqrt{\pi } b^2 \sin (2 c) S\left(\frac{2 \sqrt{d} x}{\sqrt{\pi }}\right)+2 b^2 \sqrt{d} x}{4 \sqrt{d}}","\frac{1}{2} x \left(2 a^2+b^2\right)+\frac{\sqrt{2 \pi } a b \sin (c) C\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)}{\sqrt{d}}+\frac{\sqrt{2 \pi } a b \cos (c) S\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)}{\sqrt{d}}-\frac{\sqrt{\pi } b^2 \cos (2 c) C\left(\frac{2 \sqrt{d} x}{\sqrt{\pi }}\right)}{4 \sqrt{d}}+\frac{\sqrt{\pi } b^2 \sin (2 c) S\left(\frac{2 \sqrt{d} x}{\sqrt{\pi }}\right)}{4 \sqrt{d}}",1,"(4*a^2*Sqrt[d]*x + 2*b^2*Sqrt[d]*x - b^2*Sqrt[Pi]*Cos[2*c]*FresnelC[(2*Sqrt[d]*x)/Sqrt[Pi]] + 4*a*b*Sqrt[2*Pi]*Cos[c]*FresnelS[Sqrt[d]*Sqrt[2/Pi]*x] + 4*a*b*Sqrt[2*Pi]*FresnelC[Sqrt[d]*Sqrt[2/Pi]*x]*Sin[c] + b^2*Sqrt[Pi]*FresnelS[(2*Sqrt[d]*x)/Sqrt[Pi]]*Sin[2*c])/(4*Sqrt[d])","A",1
21,1,184,187,0.5133379,"\int \frac{\left(a+b \sin \left(c+d x^2\right)\right)^2}{x^2} \, dx","Integrate[(a + b*Sin[c + d*x^2])^2/x^2,x]","\frac{-2 a^2+4 \sqrt{2 \pi } a b \sqrt{d} x \cos (c) C\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)-4 \sqrt{2 \pi } a b \sqrt{d} x \sin (c) S\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)-4 a b \sin \left(c+d x^2\right)+2 \sqrt{\pi } b^2 \sqrt{d} x \sin (2 c) C\left(\frac{2 \sqrt{d} x}{\sqrt{\pi }}\right)+2 \sqrt{\pi } b^2 \sqrt{d} x \cos (2 c) S\left(\frac{2 \sqrt{d} x}{\sqrt{\pi }}\right)+b^2 \cos \left(2 \left(c+d x^2\right)\right)-b^2}{2 x}","-\frac{2 a^2+b^2}{2 x}+2 \sqrt{2 \pi } a b \sqrt{d} \cos (c) C\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)-2 \sqrt{2 \pi } a b \sqrt{d} \sin (c) S\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)-\frac{2 a b \sin \left(c+d x^2\right)}{x}+\sqrt{\pi } b^2 \sqrt{d} \sin (2 c) C\left(\frac{2 \sqrt{d} x}{\sqrt{\pi }}\right)+\sqrt{\pi } b^2 \sqrt{d} \cos (2 c) S\left(\frac{2 \sqrt{d} x}{\sqrt{\pi }}\right)+\frac{b^2 \cos \left(2 c+2 d x^2\right)}{2 x}",1,"(-2*a^2 - b^2 + b^2*Cos[2*(c + d*x^2)] + 4*a*b*Sqrt[d]*Sqrt[2*Pi]*x*Cos[c]*FresnelC[Sqrt[d]*Sqrt[2/Pi]*x] + 2*b^2*Sqrt[d]*Sqrt[Pi]*x*Cos[2*c]*FresnelS[(2*Sqrt[d]*x)/Sqrt[Pi]] - 4*a*b*Sqrt[d]*Sqrt[2*Pi]*x*FresnelS[Sqrt[d]*Sqrt[2/Pi]*x]*Sin[c] + 2*b^2*Sqrt[d]*Sqrt[Pi]*x*FresnelC[(2*Sqrt[d]*x)/Sqrt[Pi]]*Sin[2*c] - 4*a*b*Sin[c + d*x^2])/(2*x)","A",1
22,1,226,239,0.6761866,"\int \frac{\left(a+b \sin \left(c+d x^2\right)\right)^2}{x^4} \, dx","Integrate[(a + b*Sin[c + d*x^2])^2/x^4,x]","-\frac{2 a^2+8 \sqrt{2 \pi } a b d^{3/2} x^3 \sin (c) C\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)+8 \sqrt{2 \pi } a b d^{3/2} x^3 \cos (c) S\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)+4 a b \sin \left(c+d x^2\right)+8 a b d x^2 \cos \left(c+d x^2\right)-8 \sqrt{\pi } b^2 d^{3/2} x^3 \cos (2 c) C\left(\frac{2 \sqrt{d} x}{\sqrt{\pi }}\right)+8 \sqrt{\pi } b^2 d^{3/2} x^3 \sin (2 c) S\left(\frac{2 \sqrt{d} x}{\sqrt{\pi }}\right)+4 b^2 d x^2 \sin \left(2 \left(c+d x^2\right)\right)-b^2 \cos \left(2 \left(c+d x^2\right)\right)+b^2}{6 x^3}","-\frac{2 a^2+b^2}{6 x^3}-\frac{4}{3} \sqrt{2 \pi } a b d^{3/2} \sin (c) C\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)-\frac{4}{3} \sqrt{2 \pi } a b d^{3/2} \cos (c) S\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)-\frac{4 a b d \cos \left(c+d x^2\right)}{3 x}-\frac{2 a b \sin \left(c+d x^2\right)}{3 x^3}+\frac{4}{3} \sqrt{\pi } b^2 d^{3/2} \cos (2 c) C\left(\frac{2 \sqrt{d} x}{\sqrt{\pi }}\right)-\frac{4}{3} \sqrt{\pi } b^2 d^{3/2} \sin (2 c) S\left(\frac{2 \sqrt{d} x}{\sqrt{\pi }}\right)-\frac{2 b^2 d \sin \left(2 c+2 d x^2\right)}{3 x}+\frac{b^2 \cos \left(2 c+2 d x^2\right)}{6 x^3}",1,"-1/6*(2*a^2 + b^2 + 8*a*b*d*x^2*Cos[c + d*x^2] - b^2*Cos[2*(c + d*x^2)] - 8*b^2*d^(3/2)*Sqrt[Pi]*x^3*Cos[2*c]*FresnelC[(2*Sqrt[d]*x)/Sqrt[Pi]] + 8*a*b*d^(3/2)*Sqrt[2*Pi]*x^3*Cos[c]*FresnelS[Sqrt[d]*Sqrt[2/Pi]*x] + 8*a*b*d^(3/2)*Sqrt[2*Pi]*x^3*FresnelC[Sqrt[d]*Sqrt[2/Pi]*x]*Sin[c] + 8*b^2*d^(3/2)*Sqrt[Pi]*x^3*FresnelS[(2*Sqrt[d]*x)/Sqrt[Pi]]*Sin[2*c] + 4*a*b*Sin[c + d*x^2] + 4*b^2*d*x^2*Sin[2*(c + d*x^2)])/x^3","A",1
23,1,75,117,0.2689164,"\int x^5 \sin ^3\left(a+b x^2\right) \, dx","Integrate[x^5*Sin[a + b*x^2]^3,x]","\frac{-81 \left(b^2 x^4-2\right) \cos \left(a+b x^2\right)+\left(9 b^2 x^4-2\right) \cos \left(3 \left(a+b x^2\right)\right)-6 b x^2 \left(\sin \left(3 \left(a+b x^2\right)\right)-27 \sin \left(a+b x^2\right)\right)}{216 b^3}","-\frac{\cos ^3\left(a+b x^2\right)}{27 b^3}+\frac{7 \cos \left(a+b x^2\right)}{9 b^3}+\frac{x^2 \sin ^3\left(a+b x^2\right)}{9 b^2}+\frac{2 x^2 \sin \left(a+b x^2\right)}{3 b^2}-\frac{x^4 \cos \left(a+b x^2\right)}{3 b}-\frac{x^4 \sin ^2\left(a+b x^2\right) \cos \left(a+b x^2\right)}{6 b}",1,"(-81*(-2 + b^2*x^4)*Cos[a + b*x^2] + (-2 + 9*b^2*x^4)*Cos[3*(a + b*x^2)] - 6*b*x^2*(-27*Sin[a + b*x^2] + Sin[3*(a + b*x^2)]))/(216*b^3)","A",1
24,1,58,79,0.1655577,"\int x^3 \sin ^3\left(a+b x^2\right) \, dx","Integrate[x^3*Sin[a + b*x^2]^3,x]","-\frac{-27 \sin \left(a+b x^2\right)+\sin \left(3 \left(a+b x^2\right)\right)+27 b x^2 \cos \left(a+b x^2\right)-3 b x^2 \cos \left(3 \left(a+b x^2\right)\right)}{72 b^2}","\frac{\sin ^3\left(a+b x^2\right)}{18 b^2}+\frac{\sin \left(a+b x^2\right)}{3 b^2}-\frac{x^2 \cos \left(a+b x^2\right)}{3 b}-\frac{x^2 \sin ^2\left(a+b x^2\right) \cos \left(a+b x^2\right)}{6 b}",1,"-1/72*(27*b*x^2*Cos[a + b*x^2] - 3*b*x^2*Cos[3*(a + b*x^2)] - 27*Sin[a + b*x^2] + Sin[3*(a + b*x^2)])/b^2","A",1
25,1,33,33,0.0292311,"\int x \sin ^3\left(a+b x^2\right) \, dx","Integrate[x*Sin[a + b*x^2]^3,x]","\frac{\cos \left(3 \left(a+b x^2\right)\right)}{24 b}-\frac{3 \cos \left(a+b x^2\right)}{8 b}","\frac{\cos ^3\left(a+b x^2\right)}{6 b}-\frac{\cos \left(a+b x^2\right)}{2 b}",1,"(-3*Cos[a + b*x^2])/(8*b) + Cos[3*(a + b*x^2)]/(24*b)","A",1
26,1,51,55,0.071781,"\int \frac{\sin ^3\left(a+b x^2\right)}{x} \, dx","Integrate[Sin[a + b*x^2]^3/x,x]","\frac{1}{8} \left(3 \sin (a) \text{Ci}\left(b x^2\right)-\sin (3 a) \text{Ci}\left(3 b x^2\right)+3 \cos (a) \text{Si}\left(b x^2\right)-\cos (3 a) \text{Si}\left(3 b x^2\right)\right)","\frac{3}{8} \sin (a) \text{Ci}\left(b x^2\right)-\frac{1}{8} \sin (3 a) \text{Ci}\left(3 b x^2\right)+\frac{3}{8} \cos (a) \text{Si}\left(b x^2\right)-\frac{1}{8} \cos (3 a) \text{Si}\left(3 b x^2\right)",1,"(3*CosIntegral[b*x^2]*Sin[a] - CosIntegral[3*b*x^2]*Sin[3*a] + 3*Cos[a]*SinIntegral[b*x^2] - Cos[3*a]*SinIntegral[3*b*x^2])/8","A",1
27,1,90,91,0.135071,"\int \frac{\sin ^3\left(a+b x^2\right)}{x^3} \, dx","Integrate[Sin[a + b*x^2]^3/x^3,x]","\frac{3 b x^2 \cos (a) \text{Ci}\left(b x^2\right)-3 b x^2 \cos (3 a) \text{Ci}\left(3 b x^2\right)-3 b x^2 \sin (a) \text{Si}\left(b x^2\right)+3 b x^2 \sin (3 a) \text{Si}\left(3 b x^2\right)-3 \sin \left(a+b x^2\right)+\sin \left(3 \left(a+b x^2\right)\right)}{8 x^2}","\frac{3}{8} b \cos (a) \text{Ci}\left(b x^2\right)-\frac{3}{8} b \cos (3 a) \text{Ci}\left(3 b x^2\right)-\frac{3}{8} b \sin (a) \text{Si}\left(b x^2\right)+\frac{3}{8} b \sin (3 a) \text{Si}\left(3 b x^2\right)-\frac{3 \sin \left(a+b x^2\right)}{8 x^2}+\frac{\sin \left(3 \left(a+b x^2\right)\right)}{8 x^2}",1,"(3*b*x^2*Cos[a]*CosIntegral[b*x^2] - 3*b*x^2*Cos[3*a]*CosIntegral[3*b*x^2] - 3*Sin[a + b*x^2] + Sin[3*(a + b*x^2)] - 3*b*x^2*Sin[a]*SinIntegral[b*x^2] + 3*b*x^2*Sin[3*a]*SinIntegral[3*b*x^2])/(8*x^2)","A",1
28,1,159,188,0.4404585,"\int x^2 \sin ^3\left(a+b x^2\right) \, dx","Integrate[x^2*Sin[a + b*x^2]^3,x]","\frac{27 \sqrt{2 \pi } \cos (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)-\sqrt{6 \pi } \cos (3 a) C\left(\sqrt{b} \sqrt{\frac{6}{\pi }} x\right)-27 \sqrt{2 \pi } \sin (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)+\sqrt{6 \pi } \sin (3 a) S\left(\sqrt{b} \sqrt{\frac{6}{\pi }} x\right)-54 \sqrt{b} x \cos \left(a+b x^2\right)+6 \sqrt{b} x \cos \left(3 \left(a+b x^2\right)\right)}{144 b^{3/2}}","\frac{3 \sqrt{\frac{\pi }{2}} \cos (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)}{8 b^{3/2}}-\frac{\sqrt{\frac{\pi }{6}} \cos (3 a) C\left(\sqrt{b} \sqrt{\frac{6}{\pi }} x\right)}{24 b^{3/2}}-\frac{3 \sqrt{\frac{\pi }{2}} \sin (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)}{8 b^{3/2}}+\frac{\sqrt{\frac{\pi }{6}} \sin (3 a) S\left(\sqrt{b} \sqrt{\frac{6}{\pi }} x\right)}{24 b^{3/2}}-\frac{3 x \cos \left(a+b x^2\right)}{8 b}+\frac{x \cos \left(3 a+3 b x^2\right)}{24 b}",1,"(-54*Sqrt[b]*x*Cos[a + b*x^2] + 6*Sqrt[b]*x*Cos[3*(a + b*x^2)] + 27*Sqrt[2*Pi]*Cos[a]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x] - Sqrt[6*Pi]*Cos[3*a]*FresnelC[Sqrt[b]*Sqrt[6/Pi]*x] - 27*Sqrt[2*Pi]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x]*Sin[a] + Sqrt[6*Pi]*FresnelS[Sqrt[b]*Sqrt[6/Pi]*x]*Sin[3*a])/(144*b^(3/2))","A",1
29,1,117,153,0.2333128,"\int \sin ^3\left(a+b x^2\right) \, dx","Integrate[Sin[a + b*x^2]^3,x]","\frac{\sqrt{\frac{\pi }{6}} \left(3 \sqrt{3} \sin (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)-\sin (3 a) C\left(\sqrt{b} \sqrt{\frac{6}{\pi }} x\right)+3 \sqrt{3} \cos (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)-\cos (3 a) S\left(\sqrt{b} \sqrt{\frac{6}{\pi }} x\right)\right)}{4 \sqrt{b}}","\frac{3 \sqrt{\frac{\pi }{2}} \sin (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)}{4 \sqrt{b}}-\frac{\sqrt{\frac{\pi }{6}} \sin (3 a) C\left(\sqrt{b} \sqrt{\frac{6}{\pi }} x\right)}{4 \sqrt{b}}+\frac{3 \sqrt{\frac{\pi }{2}} \cos (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)}{4 \sqrt{b}}-\frac{\sqrt{\frac{\pi }{6}} \cos (3 a) S\left(\sqrt{b} \sqrt{\frac{6}{\pi }} x\right)}{4 \sqrt{b}}",1,"(Sqrt[Pi/6]*(3*Sqrt[3]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x] - Cos[3*a]*FresnelS[Sqrt[b]*Sqrt[6/Pi]*x] + 3*Sqrt[3]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x]*Sin[a] - FresnelC[Sqrt[b]*Sqrt[6/Pi]*x]*Sin[3*a]))/(4*Sqrt[b])","A",1
30,1,167,168,0.4306697,"\int \frac{\sin ^3\left(a+b x^2\right)}{x^2} \, dx","Integrate[Sin[a + b*x^2]^3/x^2,x]","\frac{3 \sqrt{2 \pi } \sqrt{b} x \cos (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)-\sqrt{6 \pi } \sqrt{b} x \cos (3 a) C\left(\sqrt{b} \sqrt{\frac{6}{\pi }} x\right)-3 \sqrt{2 \pi } \sqrt{b} x \sin (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)+\sqrt{6 \pi } \sqrt{b} x \sin (3 a) S\left(\sqrt{b} \sqrt{\frac{6}{\pi }} x\right)-3 \sin \left(a+b x^2\right)+\sin \left(3 \left(a+b x^2\right)\right)}{4 x}","\frac{3}{2} \sqrt{\frac{\pi }{2}} \sqrt{b} \cos (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)-\frac{1}{2} \sqrt{\frac{3 \pi }{2}} \sqrt{b} \cos (3 a) C\left(\sqrt{b} \sqrt{\frac{6}{\pi }} x\right)-\frac{3}{2} \sqrt{\frac{\pi }{2}} \sqrt{b} \sin (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)+\frac{1}{2} \sqrt{\frac{3 \pi }{2}} \sqrt{b} \sin (3 a) S\left(\sqrt{b} \sqrt{\frac{6}{\pi }} x\right)-\frac{\sin ^3\left(a+b x^2\right)}{x}",1,"(3*Sqrt[b]*Sqrt[2*Pi]*x*Cos[a]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x] - Sqrt[b]*Sqrt[6*Pi]*x*Cos[3*a]*FresnelC[Sqrt[b]*Sqrt[6/Pi]*x] - 3*Sqrt[b]*Sqrt[2*Pi]*x*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x]*Sin[a] + Sqrt[b]*Sqrt[6*Pi]*x*FresnelS[Sqrt[b]*Sqrt[6/Pi]*x]*Sin[3*a] - 3*Sin[a + b*x^2] + Sin[3*(a + b*x^2)])/(4*x)","A",1
31,1,63,71,0.0663563,"\int x^2 \sin ^3\left(x^2\right) \, dx","Integrate[x^2*Sin[x^2]^3,x]","\frac{1}{144} \left(27 \sqrt{2 \pi } C\left(\sqrt{\frac{2}{\pi }} x\right)-\sqrt{6 \pi } C\left(\sqrt{\frac{6}{\pi }} x\right)+6 x \left(\cos \left(3 x^2\right)-9 \cos \left(x^2\right)\right)\right)","\frac{3}{8} \sqrt{\frac{\pi }{2}} C\left(\sqrt{\frac{2}{\pi }} x\right)-\frac{1}{24} \sqrt{\frac{\pi }{6}} C\left(\sqrt{\frac{6}{\pi }} x\right)+\frac{1}{6} x \cos ^3\left(x^2\right)-\frac{1}{2} x \cos \left(x^2\right)",1,"(6*x*(-9*Cos[x^2] + Cos[3*x^2]) + 27*Sqrt[2*Pi]*FresnelC[Sqrt[2/Pi]*x] - Sqrt[6*Pi]*FresnelC[Sqrt[6/Pi]*x])/144","A",1
32,1,75,84,0.150402,"\int x^4 \cos \left(x^2\right) \sin ^2\left(x^2\right) \, dx","Integrate[x^4*Cos[x^2]*Sin[x^2]^2,x]","\frac{1}{288} \left(-27 \sqrt{2 \pi } C\left(\sqrt{\frac{2}{\pi }} x\right)+\sqrt{6 \pi } C\left(\sqrt{\frac{6}{\pi }} x\right)+6 x \left(8 x^2 \sin ^3\left(x^2\right)+9 \cos \left(x^2\right)-\cos \left(3 x^2\right)\right)\right)","-\frac{3}{16} \sqrt{\frac{\pi }{2}} C\left(\sqrt{\frac{2}{\pi }} x\right)+\frac{1}{48} \sqrt{\frac{\pi }{6}} C\left(\sqrt{\frac{6}{\pi }} x\right)-\frac{1}{12} x \cos ^3\left(x^2\right)+\frac{1}{4} x \cos \left(x^2\right)+\frac{1}{6} x^3 \sin ^3\left(x^2\right)",1,"(-27*Sqrt[2*Pi]*FresnelC[Sqrt[2/Pi]*x] + Sqrt[6*Pi]*FresnelC[Sqrt[6/Pi]*x] + 6*x*(9*Cos[x^2] - Cos[3*x^2] + 8*x^2*Sin[x^2]^3))/288","A",1
33,1,67,67,0.0441664,"\int x \sin ^7\left(a+b x^2\right) \, dx","Integrate[x*Sin[a + b*x^2]^7,x]","-\frac{35 \cos \left(a+b x^2\right)}{128 b}+\frac{7 \cos \left(3 \left(a+b x^2\right)\right)}{128 b}-\frac{7 \cos \left(5 \left(a+b x^2\right)\right)}{640 b}+\frac{\cos \left(7 \left(a+b x^2\right)\right)}{896 b}","\frac{\cos ^7\left(a+b x^2\right)}{14 b}-\frac{3 \cos ^5\left(a+b x^2\right)}{10 b}+\frac{\cos ^3\left(a+b x^2\right)}{2 b}-\frac{\cos \left(a+b x^2\right)}{2 b}",1,"(-35*Cos[a + b*x^2])/(128*b) + (7*Cos[3*(a + b*x^2)])/(128*b) - (7*Cos[5*(a + b*x^2)])/(640*b) + Cos[7*(a + b*x^2)]/(896*b)","A",1
34,1,41,44,0.1039711,"\int \frac{\left(1+\sin \left(x^2\right)\right)^2}{x^3} \, dx","Integrate[(1 + Sin[x^2])^2/x^3,x]","\frac{4 x^2 \text{Ci}\left(x^2\right)+2 x^2 \text{Si}\left(2 x^2\right)-4 \sin \left(x^2\right)+\cos \left(2 x^2\right)-3}{4 x^2}","\text{Ci}\left(x^2\right)+\frac{\text{Si}\left(2 x^2\right)}{2}-\frac{3}{4 x^2}-\frac{\sin \left(x^2\right)}{x^2}+\frac{\cos \left(2 x^2\right)}{4 x^2}",1,"(-3 + Cos[2*x^2] + 4*x^2*CosIntegral[x^2] - 4*Sin[x^2] + 2*x^2*SinIntegral[2*x^2])/(4*x^2)","A",1
35,1,289,362,0.207363,"\int \frac{x^5}{a+b \sin \left(c+d x^2\right)} \, dx","Integrate[x^5/(a + b*Sin[c + d*x^2]),x]","\frac{-i \left(d^2 x^4 \log \left(1+\frac{i b e^{i \left(c+d x^2\right)}}{\sqrt{a^2-b^2}-a}\right)-d^2 x^4 \log \left(1-\frac{i b e^{i \left(c+d x^2\right)}}{\sqrt{a^2-b^2}+a}\right)+2 i d x^2 \text{Li}_2\left(\frac{i b e^{i \left(d x^2+c\right)}}{a+\sqrt{a^2-b^2}}\right)+2 \text{Li}_3\left(\frac{i b e^{i \left(d x^2+c\right)}}{a-\sqrt{a^2-b^2}}\right)-2 \text{Li}_3\left(\frac{i b e^{i \left(d x^2+c\right)}}{a+\sqrt{a^2-b^2}}\right)\right)-2 d x^2 \text{Li}_2\left(-\frac{i b e^{i \left(d x^2+c\right)}}{\sqrt{a^2-b^2}-a}\right)}{2 d^3 \sqrt{a^2-b^2}}","-\frac{i \text{Li}_3\left(\frac{i b e^{i \left(d x^2+c\right)}}{a-\sqrt{a^2-b^2}}\right)}{d^3 \sqrt{a^2-b^2}}+\frac{i \text{Li}_3\left(\frac{i b e^{i \left(d x^2+c\right)}}{a+\sqrt{a^2-b^2}}\right)}{d^3 \sqrt{a^2-b^2}}-\frac{x^2 \text{Li}_2\left(\frac{i b e^{i \left(d x^2+c\right)}}{a-\sqrt{a^2-b^2}}\right)}{d^2 \sqrt{a^2-b^2}}+\frac{x^2 \text{Li}_2\left(\frac{i b e^{i \left(d x^2+c\right)}}{a+\sqrt{a^2-b^2}}\right)}{d^2 \sqrt{a^2-b^2}}-\frac{i x^4 \log \left(1-\frac{i b e^{i \left(c+d x^2\right)}}{a-\sqrt{a^2-b^2}}\right)}{2 d \sqrt{a^2-b^2}}+\frac{i x^4 \log \left(1-\frac{i b e^{i \left(c+d x^2\right)}}{\sqrt{a^2-b^2}+a}\right)}{2 d \sqrt{a^2-b^2}}",1,"(-2*d*x^2*PolyLog[2, ((-I)*b*E^(I*(c + d*x^2)))/(-a + Sqrt[a^2 - b^2])] - I*(d^2*x^4*Log[1 + (I*b*E^(I*(c + d*x^2)))/(-a + Sqrt[a^2 - b^2])] - d^2*x^4*Log[1 - (I*b*E^(I*(c + d*x^2)))/(a + Sqrt[a^2 - b^2])] + (2*I)*d*x^2*PolyLog[2, (I*b*E^(I*(c + d*x^2)))/(a + Sqrt[a^2 - b^2])] + 2*PolyLog[3, (I*b*E^(I*(c + d*x^2)))/(a - Sqrt[a^2 - b^2])] - 2*PolyLog[3, (I*b*E^(I*(c + d*x^2)))/(a + Sqrt[a^2 - b^2])]))/(2*Sqrt[a^2 - b^2]*d^3)","A",1
36,1,188,245,0.0671348,"\int \frac{x^3}{a+b \sin \left(c+d x^2\right)} \, dx","Integrate[x^3/(a + b*Sin[c + d*x^2]),x]","\frac{-\text{Li}_2\left(-\frac{i b e^{i \left(d x^2+c\right)}}{\sqrt{a^2-b^2}-a}\right)+\text{Li}_2\left(\frac{i b e^{i \left(d x^2+c\right)}}{a+\sqrt{a^2-b^2}}\right)-i d x^2 \left(\log \left(1+\frac{i b e^{i \left(c+d x^2\right)}}{\sqrt{a^2-b^2}-a}\right)-\log \left(1-\frac{i b e^{i \left(c+d x^2\right)}}{\sqrt{a^2-b^2}+a}\right)\right)}{2 d^2 \sqrt{a^2-b^2}}","-\frac{\text{Li}_2\left(\frac{i b e^{i \left(d x^2+c\right)}}{a-\sqrt{a^2-b^2}}\right)}{2 d^2 \sqrt{a^2-b^2}}+\frac{\text{Li}_2\left(\frac{i b e^{i \left(d x^2+c\right)}}{a+\sqrt{a^2-b^2}}\right)}{2 d^2 \sqrt{a^2-b^2}}-\frac{i x^2 \log \left(1-\frac{i b e^{i \left(c+d x^2\right)}}{a-\sqrt{a^2-b^2}}\right)}{2 d \sqrt{a^2-b^2}}+\frac{i x^2 \log \left(1-\frac{i b e^{i \left(c+d x^2\right)}}{\sqrt{a^2-b^2}+a}\right)}{2 d \sqrt{a^2-b^2}}",1,"((-I)*d*x^2*(Log[1 + (I*b*E^(I*(c + d*x^2)))/(-a + Sqrt[a^2 - b^2])] - Log[1 - (I*b*E^(I*(c + d*x^2)))/(a + Sqrt[a^2 - b^2])]) - PolyLog[2, ((-I)*b*E^(I*(c + d*x^2)))/(-a + Sqrt[a^2 - b^2])] + PolyLog[2, (I*b*E^(I*(c + d*x^2)))/(a + Sqrt[a^2 - b^2])])/(2*Sqrt[a^2 - b^2]*d^2)","A",1
37,1,48,48,0.0850255,"\int \frac{x}{a+b \sin \left(c+d x^2\right)} \, dx","Integrate[x/(a + b*Sin[c + d*x^2]),x]","\frac{\tan ^{-1}\left(\frac{a \tan \left(\frac{1}{2} \left(c+d x^2\right)\right)+b}{\sqrt{a^2-b^2}}\right)}{d \sqrt{a^2-b^2}}","\frac{\tan ^{-1}\left(\frac{a \tan \left(\frac{1}{2} \left(c+d x^2\right)\right)+b}{\sqrt{a^2-b^2}}\right)}{d \sqrt{a^2-b^2}}",1,"ArcTan[(b + a*Tan[(c + d*x^2)/2])/Sqrt[a^2 - b^2]]/(Sqrt[a^2 - b^2]*d)","A",1
38,0,0,21,0.4000107,"\int \frac{1}{x \left(a+b \sin \left(c+d x^2\right)\right)} \, dx","Integrate[1/(x*(a + b*Sin[c + d*x^2])),x]","\int \frac{1}{x \left(a+b \sin \left(c+d x^2\right)\right)} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \sin \left(c+d x^2\right)\right)},x\right)",0,"Integrate[1/(x*(a + b*Sin[c + d*x^2])), x]","A",-1
39,0,0,21,0.3511295,"\int \frac{1}{x^3 \left(a+b \sin \left(c+d x^2\right)\right)} \, dx","Integrate[1/(x^3*(a + b*Sin[c + d*x^2])),x]","\int \frac{1}{x^3 \left(a+b \sin \left(c+d x^2\right)\right)} \, dx","\text{Int}\left(\frac{1}{x^3 \left(a+b \sin \left(c+d x^2\right)\right)},x\right)",0,"Integrate[1/(x^3*(a + b*Sin[c + d*x^2])), x]","A",-1
40,0,0,21,0.3818441,"\int \frac{x^2}{a+b \sin \left(c+d x^2\right)} \, dx","Integrate[x^2/(a + b*Sin[c + d*x^2]),x]","\int \frac{x^2}{a+b \sin \left(c+d x^2\right)} \, dx","\text{Int}\left(\frac{x^2}{a+b \sin \left(c+d x^2\right)},x\right)",0,"Integrate[x^2/(a + b*Sin[c + d*x^2]), x]","A",-1
41,0,0,17,0.0239569,"\int \frac{1}{a+b \sin \left(c+d x^2\right)} \, dx","Integrate[(a + b*Sin[c + d*x^2])^(-1),x]","\int \frac{1}{a+b \sin \left(c+d x^2\right)} \, dx","\text{Int}\left(\frac{1}{a+b \sin \left(c+d x^2\right)},x\right)",0,"Integrate[(a + b*Sin[c + d*x^2])^(-1), x]","A",-1
42,0,0,21,0.2530346,"\int \frac{1}{x^2 \left(a+b \sin \left(c+d x^2\right)\right)} \, dx","Integrate[1/(x^2*(a + b*Sin[c + d*x^2])),x]","\int \frac{1}{x^2 \left(a+b \sin \left(c+d x^2\right)\right)} \, dx","\text{Int}\left(\frac{1}{x^2 \left(a+b \sin \left(c+d x^2\right)\right)},x\right)",0,"Integrate[1/(x^2*(a + b*Sin[c + d*x^2])), x]","A",-1
43,1,513,663,2.3343025,"\int \frac{x^5}{\left(a+b \sin \left(c+d x^2\right)\right)^2} \, dx","Integrate[x^5/(a + b*Sin[c + d*x^2])^2,x]","\frac{-\frac{i a d^2 x^4 \log \left(1+\frac{i b e^{i \left(c+d x^2\right)}}{\sqrt{a^2-b^2}-a}\right)}{\sqrt{a^2-b^2}}+\frac{i a d^2 x^4 \log \left(1-\frac{i b e^{i \left(c+d x^2\right)}}{\sqrt{a^2-b^2}+a}\right)}{\sqrt{a^2-b^2}}+\left(-\frac{2 a d x^2}{\sqrt{a^2-b^2}}+2 i\right) \text{Li}_2\left(-\frac{i b e^{i \left(d x^2+c\right)}}{\sqrt{a^2-b^2}-a}\right)+\left(\frac{2 a d x^2}{\sqrt{a^2-b^2}}+2 i\right) \text{Li}_2\left(\frac{i b e^{i \left(d x^2+c\right)}}{a+\sqrt{a^2-b^2}}\right)-\frac{2 i a \text{Li}_3\left(\frac{i b e^{i \left(d x^2+c\right)}}{a-\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}+\frac{2 i a \text{Li}_3\left(\frac{i b e^{i \left(d x^2+c\right)}}{a+\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}-2 d x^2 \log \left(1+\frac{i b e^{i \left(c+d x^2\right)}}{\sqrt{a^2-b^2}-a}\right)-2 d x^2 \log \left(1-\frac{i b e^{i \left(c+d x^2\right)}}{\sqrt{a^2-b^2}+a}\right)+\frac{b d^2 x^4 \cos \left(c+d x^2\right)}{a+b \sin \left(c+d x^2\right)}+i d^2 x^4}{2 d^3 \left(a^2-b^2\right)}","\frac{i \text{Li}_2\left(\frac{i b e^{i \left(d x^2+c\right)}}{a-\sqrt{a^2-b^2}}\right)}{d^3 \left(a^2-b^2\right)}+\frac{i \text{Li}_2\left(\frac{i b e^{i \left(d x^2+c\right)}}{a+\sqrt{a^2-b^2}}\right)}{d^3 \left(a^2-b^2\right)}-\frac{i a \text{Li}_3\left(\frac{i b e^{i \left(d x^2+c\right)}}{a-\sqrt{a^2-b^2}}\right)}{d^3 \left(a^2-b^2\right)^{3/2}}+\frac{i a \text{Li}_3\left(\frac{i b e^{i \left(d x^2+c\right)}}{a+\sqrt{a^2-b^2}}\right)}{d^3 \left(a^2-b^2\right)^{3/2}}-\frac{a x^2 \text{Li}_2\left(\frac{i b e^{i \left(d x^2+c\right)}}{a-\sqrt{a^2-b^2}}\right)}{d^2 \left(a^2-b^2\right)^{3/2}}+\frac{a x^2 \text{Li}_2\left(\frac{i b e^{i \left(d x^2+c\right)}}{a+\sqrt{a^2-b^2}}\right)}{d^2 \left(a^2-b^2\right)^{3/2}}-\frac{x^2 \log \left(1-\frac{i b e^{i \left(c+d x^2\right)}}{a-\sqrt{a^2-b^2}}\right)}{d^2 \left(a^2-b^2\right)}-\frac{x^2 \log \left(1-\frac{i b e^{i \left(c+d x^2\right)}}{\sqrt{a^2-b^2}+a}\right)}{d^2 \left(a^2-b^2\right)}-\frac{i a x^4 \log \left(1-\frac{i b e^{i \left(c+d x^2\right)}}{a-\sqrt{a^2-b^2}}\right)}{2 d \left(a^2-b^2\right)^{3/2}}+\frac{i a x^4 \log \left(1-\frac{i b e^{i \left(c+d x^2\right)}}{\sqrt{a^2-b^2}+a}\right)}{2 d \left(a^2-b^2\right)^{3/2}}+\frac{b x^4 \cos \left(c+d x^2\right)}{2 d \left(a^2-b^2\right) \left(a+b \sin \left(c+d x^2\right)\right)}+\frac{i x^4}{2 d \left(a^2-b^2\right)}",1,"(I*d^2*x^4 - 2*d*x^2*Log[1 + (I*b*E^(I*(c + d*x^2)))/(-a + Sqrt[a^2 - b^2])] - (I*a*d^2*x^4*Log[1 + (I*b*E^(I*(c + d*x^2)))/(-a + Sqrt[a^2 - b^2])])/Sqrt[a^2 - b^2] - 2*d*x^2*Log[1 - (I*b*E^(I*(c + d*x^2)))/(a + Sqrt[a^2 - b^2])] + (I*a*d^2*x^4*Log[1 - (I*b*E^(I*(c + d*x^2)))/(a + Sqrt[a^2 - b^2])])/Sqrt[a^2 - b^2] + (2*I - (2*a*d*x^2)/Sqrt[a^2 - b^2])*PolyLog[2, ((-I)*b*E^(I*(c + d*x^2)))/(-a + Sqrt[a^2 - b^2])] + (2*I + (2*a*d*x^2)/Sqrt[a^2 - b^2])*PolyLog[2, (I*b*E^(I*(c + d*x^2)))/(a + Sqrt[a^2 - b^2])] - ((2*I)*a*PolyLog[3, (I*b*E^(I*(c + d*x^2)))/(a - Sqrt[a^2 - b^2])])/Sqrt[a^2 - b^2] + ((2*I)*a*PolyLog[3, (I*b*E^(I*(c + d*x^2)))/(a + Sqrt[a^2 - b^2])])/Sqrt[a^2 - b^2] + (b*d^2*x^4*Cos[c + d*x^2])/(a + b*Sin[c + d*x^2]))/(2*(a^2 - b^2)*d^3)","A",1
44,1,302,324,0.9555671,"\int \frac{x^3}{\left(a+b \sin \left(c+d x^2\right)\right)^2} \, dx","Integrate[x^3/(a + b*Sin[c + d*x^2])^2,x]","\frac{-\frac{a \text{Li}_2\left(-\frac{i b e^{i \left(d x^2+c\right)}}{\sqrt{a^2-b^2}-a}\right)}{\left(a^2-b^2\right)^{3/2}}+\frac{a \text{Li}_2\left(\frac{i b e^{i \left(d x^2+c\right)}}{a+\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{3/2}}-\frac{i a d x^2 \log \left(1+\frac{i b e^{i \left(c+d x^2\right)}}{\sqrt{a^2-b^2}-a}\right)}{\left(a^2-b^2\right)^{3/2}}+\frac{i a d x^2 \log \left(1-\frac{i b e^{i \left(c+d x^2\right)}}{\sqrt{a^2-b^2}+a}\right)}{\left(a^2-b^2\right)^{3/2}}-\frac{\log \left(a+b \sin \left(c+d x^2\right)\right)}{a^2-b^2}+\frac{b d x^2 \cos \left(c+d x^2\right)}{\left(a^2-b^2\right) \left(a+b \sin \left(c+d x^2\right)\right)}}{2 d^2}","-\frac{a \text{Li}_2\left(\frac{i b e^{i \left(d x^2+c\right)}}{a-\sqrt{a^2-b^2}}\right)}{2 d^2 \left(a^2-b^2\right)^{3/2}}+\frac{a \text{Li}_2\left(\frac{i b e^{i \left(d x^2+c\right)}}{a+\sqrt{a^2-b^2}}\right)}{2 d^2 \left(a^2-b^2\right)^{3/2}}-\frac{\log \left(a+b \sin \left(c+d x^2\right)\right)}{2 d^2 \left(a^2-b^2\right)}-\frac{i a x^2 \log \left(1-\frac{i b e^{i \left(c+d x^2\right)}}{a-\sqrt{a^2-b^2}}\right)}{2 d \left(a^2-b^2\right)^{3/2}}+\frac{i a x^2 \log \left(1-\frac{i b e^{i \left(c+d x^2\right)}}{\sqrt{a^2-b^2}+a}\right)}{2 d \left(a^2-b^2\right)^{3/2}}+\frac{b x^2 \cos \left(c+d x^2\right)}{2 d \left(a^2-b^2\right) \left(a+b \sin \left(c+d x^2\right)\right)}",1,"(((-I)*a*d*x^2*Log[1 + (I*b*E^(I*(c + d*x^2)))/(-a + Sqrt[a^2 - b^2])])/(a^2 - b^2)^(3/2) + (I*a*d*x^2*Log[1 - (I*b*E^(I*(c + d*x^2)))/(a + Sqrt[a^2 - b^2])])/(a^2 - b^2)^(3/2) - Log[a + b*Sin[c + d*x^2]]/(a^2 - b^2) - (a*PolyLog[2, ((-I)*b*E^(I*(c + d*x^2)))/(-a + Sqrt[a^2 - b^2])])/(a^2 - b^2)^(3/2) + (a*PolyLog[2, (I*b*E^(I*(c + d*x^2)))/(a + Sqrt[a^2 - b^2])])/(a^2 - b^2)^(3/2) + (b*d*x^2*Cos[c + d*x^2])/((a^2 - b^2)*(a + b*Sin[c + d*x^2])))/(2*d^2)","A",1
45,1,91,91,0.19804,"\int \frac{x}{\left(a+b \sin \left(c+d x^2\right)\right)^2} \, dx","Integrate[x/(a + b*Sin[c + d*x^2])^2,x]","\frac{\frac{2 a \tan ^{-1}\left(\frac{a \tan \left(\frac{1}{2} \left(c+d x^2\right)\right)+b}{\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}+\frac{b \cos \left(c+d x^2\right)}{a+b \sin \left(c+d x^2\right)}}{2 d (a-b) (a+b)}","\frac{a \tan ^{-1}\left(\frac{a \tan \left(\frac{1}{2} \left(c+d x^2\right)\right)+b}{\sqrt{a^2-b^2}}\right)}{d \left(a^2-b^2\right)^{3/2}}+\frac{b \cos \left(c+d x^2\right)}{2 d \left(a^2-b^2\right) \left(a+b \sin \left(c+d x^2\right)\right)}",1,"((2*a*ArcTan[(b + a*Tan[(c + d*x^2)/2])/Sqrt[a^2 - b^2]])/Sqrt[a^2 - b^2] + (b*Cos[c + d*x^2])/(a + b*Sin[c + d*x^2]))/(2*(a - b)*(a + b)*d)","A",1
46,0,0,21,6.5578969,"\int \frac{1}{x \left(a+b \sin \left(c+d x^2\right)\right)^2} \, dx","Integrate[1/(x*(a + b*Sin[c + d*x^2])^2),x]","\int \frac{1}{x \left(a+b \sin \left(c+d x^2\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \sin \left(c+d x^2\right)\right)^2},x\right)",0,"Integrate[1/(x*(a + b*Sin[c + d*x^2])^2), x]","A",-1
47,0,0,21,8.833808,"\int \frac{1}{x^3 \left(a+b \sin \left(c+d x^2\right)\right)^2} \, dx","Integrate[1/(x^3*(a + b*Sin[c + d*x^2])^2),x]","\int \frac{1}{x^3 \left(a+b \sin \left(c+d x^2\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x^3 \left(a+b \sin \left(c+d x^2\right)\right)^2},x\right)",0,"Integrate[1/(x^3*(a + b*Sin[c + d*x^2])^2), x]","A",-1
48,0,0,21,4.3585448,"\int \frac{x^2}{\left(a+b \sin \left(c+d x^2\right)\right)^2} \, dx","Integrate[x^2/(a + b*Sin[c + d*x^2])^2,x]","\int \frac{x^2}{\left(a+b \sin \left(c+d x^2\right)\right)^2} \, dx","\text{Int}\left(\frac{x^2}{\left(a+b \sin \left(c+d x^2\right)\right)^2},x\right)",0,"Integrate[x^2/(a + b*Sin[c + d*x^2])^2, x]","A",-1
49,0,0,17,5.0634971,"\int \frac{1}{\left(a+b \sin \left(c+d x^2\right)\right)^2} \, dx","Integrate[(a + b*Sin[c + d*x^2])^(-2),x]","\int \frac{1}{\left(a+b \sin \left(c+d x^2\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{\left(a+b \sin \left(c+d x^2\right)\right)^2},x\right)",0,"Integrate[(a + b*Sin[c + d*x^2])^(-2), x]","A",-1
50,0,0,21,7.7814609,"\int \frac{1}{x^2 \left(a+b \sin \left(c+d x^2\right)\right)^2} \, dx","Integrate[1/(x^2*(a + b*Sin[c + d*x^2])^2),x]","\int \frac{1}{x^2 \left(a+b \sin \left(c+d x^2\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x^2 \left(a+b \sin \left(c+d x^2\right)\right)^2},x\right)",0,"Integrate[1/(x^2*(a + b*Sin[c + d*x^2])^2), x]","A",-1
51,0,0,23,0.9217649,"\int (e x)^m \left(a+b \sin \left(c+d x^2\right)\right)^p \, dx","Integrate[(e*x)^m*(a + b*Sin[c + d*x^2])^p,x]","\int (e x)^m \left(a+b \sin \left(c+d x^2\right)\right)^p \, dx","\text{Int}\left((e x)^m \left(a+b \sin \left(c+d x^2\right)\right)^p,x\right)",0,"Integrate[(e*x)^m*(a + b*Sin[c + d*x^2])^p, x]","A",-1
52,1,373,444,8.6051636,"\int (e x)^m \left(a+b \sin \left(c+d x^2\right)\right)^3 \, dx","Integrate[(e*x)^m*(a + b*Sin[c + d*x^2])^3,x]","\frac{1}{16} i x (e x)^m \left(3 b e^{i c} \left(4 a^2+b^2\right) \left(-i d x^2\right)^{-\frac{m}{2}-\frac{1}{2}} \Gamma \left(\frac{m+1}{2},-i d x^2\right)-3 b e^{-i c} \left(4 a^2+b^2\right) \left(i d x^2\right)^{-\frac{m}{2}-\frac{1}{2}} \Gamma \left(\frac{m+1}{2},i d x^2\right)-\frac{8 i a \left(2 a^2+3 b^2\right)}{m+1}-3 i a b^2 e^{2 i c} 2^{\frac{1}{2}-\frac{m}{2}} \left(-i d x^2\right)^{-\frac{m}{2}-\frac{1}{2}} \Gamma \left(\frac{m+1}{2},-2 i d x^2\right)-3 i a b^2 e^{-2 i c} 2^{\frac{1}{2}-\frac{m}{2}} \left(i d x^2\right)^{-\frac{m}{2}-\frac{1}{2}} \Gamma \left(\frac{m+1}{2},2 i d x^2\right)-b^3 e^{3 i c} 3^{-\frac{m}{2}-\frac{1}{2}} \left(-i d x^2\right)^{-\frac{m}{2}-\frac{1}{2}} \Gamma \left(\frac{m+1}{2},-3 i d x^2\right)+b^3 e^{-3 i c} 3^{-\frac{m}{2}-\frac{1}{2}} \left(i d x^2\right)^{-\frac{m}{2}-\frac{1}{2}} \Gamma \left(\frac{m+1}{2},3 i d x^2\right)\right)","\frac{3 i b e^{i c} \left(4 a^2+b^2\right) \left(-i d x^2\right)^{\frac{1}{2} (-m-1)} (e x)^{m+1} \Gamma \left(\frac{m+1}{2},-i d x^2\right)}{16 e}-\frac{3 i b e^{-i c} \left(4 a^2+b^2\right) \left(i d x^2\right)^{\frac{1}{2} (-m-1)} (e x)^{m+1} \Gamma \left(\frac{m+1}{2},i d x^2\right)}{16 e}+\frac{a \left(2 a^2+3 b^2\right) (e x)^{m+1}}{2 e (m+1)}+\frac{3 a b^2 e^{2 i c} 2^{-\frac{m}{2}-\frac{7}{2}} \left(-i d x^2\right)^{\frac{1}{2} (-m-1)} (e x)^{m+1} \Gamma \left(\frac{m+1}{2},-2 i d x^2\right)}{e}+\frac{3 a b^2 e^{-2 i c} 2^{-\frac{m}{2}-\frac{7}{2}} \left(i d x^2\right)^{\frac{1}{2} (-m-1)} (e x)^{m+1} \Gamma \left(\frac{m+1}{2},2 i d x^2\right)}{e}-\frac{i b^3 e^{3 i c} 3^{-\frac{m}{2}-\frac{1}{2}} \left(-i d x^2\right)^{\frac{1}{2} (-m-1)} (e x)^{m+1} \Gamma \left(\frac{m+1}{2},-3 i d x^2\right)}{16 e}+\frac{i b^3 e^{-3 i c} 3^{-\frac{m}{2}-\frac{1}{2}} \left(i d x^2\right)^{\frac{1}{2} (-m-1)} (e x)^{m+1} \Gamma \left(\frac{m+1}{2},3 i d x^2\right)}{16 e}",1,"(I/16)*x*(e*x)^m*(((-8*I)*a*(2*a^2 + 3*b^2))/(1 + m) + 3*b*(4*a^2 + b^2)*E^(I*c)*((-I)*d*x^2)^(-1/2 - m/2)*Gamma[(1 + m)/2, (-I)*d*x^2] - (3*b*(4*a^2 + b^2)*(I*d*x^2)^(-1/2 - m/2)*Gamma[(1 + m)/2, I*d*x^2])/E^(I*c) - (3*I)*2^(1/2 - m/2)*a*b^2*E^((2*I)*c)*((-I)*d*x^2)^(-1/2 - m/2)*Gamma[(1 + m)/2, (-2*I)*d*x^2] - ((3*I)*2^(1/2 - m/2)*a*b^2*(I*d*x^2)^(-1/2 - m/2)*Gamma[(1 + m)/2, (2*I)*d*x^2])/E^((2*I)*c) - 3^(-1/2 - m/2)*b^3*E^((3*I)*c)*((-I)*d*x^2)^(-1/2 - m/2)*Gamma[(1 + m)/2, (-3*I)*d*x^2] + (3^(-1/2 - m/2)*b^3*(I*d*x^2)^(-1/2 - m/2)*Gamma[(1 + m)/2, (3*I)*d*x^2])/E^((3*I)*c))","A",1
53,1,551,279,6.5834558,"\int (e x)^m \left(a+b \sin \left(c+d x^2\right)\right)^2 \, dx","Integrate[(e*x)^m*(a + b*Sin[c + d*x^2])^2,x]","\frac{2^{\frac{1}{2} (-m-7)} x \left(d^2 x^4\right)^{\frac{1}{2} (-m-1)} (e x)^m \left(a^2 2^{\frac{m+7}{2}} \left(d^2 x^4\right)^{\frac{m+1}{2}}-i a b 2^{\frac{m+5}{2}} (m+1) (\cos (c)-i \sin (c)) \left(-i d x^2\right)^{\frac{m+1}{2}} \Gamma \left(\frac{m+1}{2},i d x^2\right)+i a b 2^{\frac{m+5}{2}} (m+1) (\cos (c)+i \sin (c)) \left(i d x^2\right)^{\frac{m+1}{2}} \Gamma \left(\frac{m+1}{2},-i d x^2\right)+b^2 \cos (2 c) \left(-i d x^2\right)^{\frac{m+1}{2}} \Gamma \left(\frac{m+1}{2},2 i d x^2\right)+b^2 m \cos (2 c) \left(-i d x^2\right)^{\frac{m+1}{2}} \Gamma \left(\frac{m+1}{2},2 i d x^2\right)+b^2 \cos (2 c) \left(i d x^2\right)^{\frac{m+1}{2}} \Gamma \left(\frac{m+1}{2},-2 i d x^2\right)+b^2 m \cos (2 c) \left(i d x^2\right)^{\frac{m+1}{2}} \Gamma \left(\frac{m+1}{2},-2 i d x^2\right)-i b^2 \sin (2 c) \left(-i d x^2\right)^{\frac{m+1}{2}} \Gamma \left(\frac{m+1}{2},2 i d x^2\right)-i b^2 m \sin (2 c) \left(-i d x^2\right)^{\frac{m+1}{2}} \Gamma \left(\frac{m+1}{2},2 i d x^2\right)+i b^2 \sin (2 c) \left(i d x^2\right)^{\frac{m+1}{2}} \Gamma \left(\frac{m+1}{2},-2 i d x^2\right)+i b^2 m \sin (2 c) \left(i d x^2\right)^{\frac{m+1}{2}} \Gamma \left(\frac{m+1}{2},-2 i d x^2\right)+b^2 2^{\frac{m+5}{2}} \left(d^2 x^4\right)^{\frac{m+1}{2}}\right)}{m+1}","\frac{\left(2 a^2+b^2\right) (e x)^{m+1}}{2 e (m+1)}+\frac{i a b e^{i c} \left(-i d x^2\right)^{\frac{1}{2} (-m-1)} (e x)^{m+1} \Gamma \left(\frac{m+1}{2},-i d x^2\right)}{2 e}-\frac{i a b e^{-i c} \left(i d x^2\right)^{\frac{1}{2} (-m-1)} (e x)^{m+1} \Gamma \left(\frac{m+1}{2},i d x^2\right)}{2 e}+\frac{b^2 e^{2 i c} 2^{-\frac{m}{2}-\frac{7}{2}} \left(-i d x^2\right)^{\frac{1}{2} (-m-1)} (e x)^{m+1} \Gamma \left(\frac{m+1}{2},-2 i d x^2\right)}{e}+\frac{b^2 e^{-2 i c} 2^{-\frac{m}{2}-\frac{7}{2}} \left(i d x^2\right)^{\frac{1}{2} (-m-1)} (e x)^{m+1} \Gamma \left(\frac{m+1}{2},2 i d x^2\right)}{e}",1,"(2^((-7 - m)/2)*x*(e*x)^m*(d^2*x^4)^((-1 - m)/2)*(2^((7 + m)/2)*a^2*(d^2*x^4)^((1 + m)/2) + 2^((5 + m)/2)*b^2*(d^2*x^4)^((1 + m)/2) + b^2*(I*d*x^2)^((1 + m)/2)*Cos[2*c]*Gamma[(1 + m)/2, (-2*I)*d*x^2] + b^2*m*(I*d*x^2)^((1 + m)/2)*Cos[2*c]*Gamma[(1 + m)/2, (-2*I)*d*x^2] + b^2*((-I)*d*x^2)^((1 + m)/2)*Cos[2*c]*Gamma[(1 + m)/2, (2*I)*d*x^2] + b^2*m*((-I)*d*x^2)^((1 + m)/2)*Cos[2*c]*Gamma[(1 + m)/2, (2*I)*d*x^2] - I*2^((5 + m)/2)*a*b*(1 + m)*((-I)*d*x^2)^((1 + m)/2)*Gamma[(1 + m)/2, I*d*x^2]*(Cos[c] - I*Sin[c]) + I*2^((5 + m)/2)*a*b*(1 + m)*(I*d*x^2)^((1 + m)/2)*Gamma[(1 + m)/2, (-I)*d*x^2]*(Cos[c] + I*Sin[c]) + I*b^2*(I*d*x^2)^((1 + m)/2)*Gamma[(1 + m)/2, (-2*I)*d*x^2]*Sin[2*c] + I*b^2*m*(I*d*x^2)^((1 + m)/2)*Gamma[(1 + m)/2, (-2*I)*d*x^2]*Sin[2*c] - I*b^2*((-I)*d*x^2)^((1 + m)/2)*Gamma[(1 + m)/2, (2*I)*d*x^2]*Sin[2*c] - I*b^2*m*((-I)*d*x^2)^((1 + m)/2)*Gamma[(1 + m)/2, (2*I)*d*x^2]*Sin[2*c]))/(1 + m)","A",1
54,1,149,134,1.5138885,"\int (e x)^m \left(a+b \sin \left(c+d x^2\right)\right) \, dx","Integrate[(e*x)^m*(a + b*Sin[c + d*x^2]),x]","\frac{x \left(d^2 x^4\right)^{\frac{1}{2} (-m-1)} (e x)^m \left(4 a \left(d^2 x^4\right)^{\frac{m+1}{2}}-i b (m+1) (\cos (c)-i \sin (c)) \left(-i d x^2\right)^{\frac{m+1}{2}} \Gamma \left(\frac{m+1}{2},i d x^2\right)+i b (m+1) (\cos (c)+i \sin (c)) \left(i d x^2\right)^{\frac{m+1}{2}} \Gamma \left(\frac{m+1}{2},-i d x^2\right)\right)}{4 (m+1)}","\frac{a (e x)^{m+1}}{e (m+1)}+\frac{i b e^{i c} \left(-i d x^2\right)^{\frac{1}{2} (-m-1)} (e x)^{m+1} \Gamma \left(\frac{m+1}{2},-i d x^2\right)}{4 e}-\frac{i b e^{-i c} \left(i d x^2\right)^{\frac{1}{2} (-m-1)} (e x)^{m+1} \Gamma \left(\frac{m+1}{2},i d x^2\right)}{4 e}",1,"(x*(e*x)^m*(d^2*x^4)^((-1 - m)/2)*(4*a*(d^2*x^4)^((1 + m)/2) - I*b*(1 + m)*((-I)*d*x^2)^((1 + m)/2)*Gamma[(1 + m)/2, I*d*x^2]*(Cos[c] - I*Sin[c]) + I*b*(1 + m)*(I*d*x^2)^((1 + m)/2)*Gamma[(1 + m)/2, (-I)*d*x^2]*(Cos[c] + I*Sin[c])))/(4*(1 + m))","A",1
55,0,0,23,0.3903393,"\int \frac{(e x)^m}{a+b \sin \left(c+d x^2\right)} \, dx","Integrate[(e*x)^m/(a + b*Sin[c + d*x^2]),x]","\int \frac{(e x)^m}{a+b \sin \left(c+d x^2\right)} \, dx","\text{Int}\left(\frac{(e x)^m}{a+b \sin \left(c+d x^2\right)},x\right)",0,"Integrate[(e*x)^m/(a + b*Sin[c + d*x^2]), x]","A",-1
56,0,0,23,0.9112305,"\int \frac{(e x)^m}{\left(a+b \sin \left(c+d x^2\right)\right)^2} \, dx","Integrate[(e*x)^m/(a + b*Sin[c + d*x^2])^2,x]","\int \frac{(e x)^m}{\left(a+b \sin \left(c+d x^2\right)\right)^2} \, dx","\text{Int}\left(\frac{(e x)^m}{\left(a+b \sin \left(c+d x^2\right)\right)^2},x\right)",0,"Integrate[(e*x)^m/(a + b*Sin[c + d*x^2])^2, x]","A",-1
57,1,44,44,0.0089808,"\int x^5 \left(a+b \sin \left(c+d x^3\right)\right) \, dx","Integrate[x^5*(a + b*Sin[c + d*x^3]),x]","\frac{a x^6}{6}+\frac{b \sin \left(c+d x^3\right)}{3 d^2}-\frac{b x^3 \cos \left(c+d x^3\right)}{3 d}","\frac{a x^6}{6}+\frac{b \sin \left(c+d x^3\right)}{3 d^2}-\frac{b x^3 \cos \left(c+d x^3\right)}{3 d}",1,"(a*x^6)/6 - (b*x^3*Cos[c + d*x^3])/(3*d) + (b*Sin[c + d*x^3])/(3*d^2)","A",1
58,1,41,25,0.0216439,"\int x^2 \left(a+b \sin \left(c+d x^3\right)\right) \, dx","Integrate[x^2*(a + b*Sin[c + d*x^3]),x]","\frac{a x^3}{3}+\frac{b \sin (c) \sin \left(d x^3\right)}{3 d}-\frac{b \cos (c) \cos \left(d x^3\right)}{3 d}","\frac{a x^3}{3}-\frac{b \cos \left(c+d x^3\right)}{3 d}",1,"(a*x^3)/3 - (b*Cos[c]*Cos[d*x^3])/(3*d) + (b*Sin[c]*Sin[d*x^3])/(3*d)","A",1
59,1,29,31,0.0505649,"\int \frac{a+b \sin \left(c+d x^3\right)}{x} \, dx","Integrate[(a + b*Sin[c + d*x^3])/x,x]","a \log (x)+\frac{1}{3} b \left(\sin (c) \text{Ci}\left(d x^3\right)+\cos (c) \text{Si}\left(d x^3\right)\right)","a \log (x)+\frac{1}{3} b \sin (c) \text{Ci}\left(d x^3\right)+\frac{1}{3} b \cos (c) \text{Si}\left(d x^3\right)",1,"a*Log[x] + (b*(CosIntegral[d*x^3]*Sin[c] + Cos[c]*SinIntegral[d*x^3]))/3","A",1
60,1,48,53,0.0880744,"\int \frac{a+b \sin \left(c+d x^3\right)}{x^4} \, dx","Integrate[(a + b*Sin[c + d*x^3])/x^4,x]","-\frac{a-b d x^3 \cos (c) \text{Ci}\left(d x^3\right)+b d x^3 \sin (c) \text{Si}\left(d x^3\right)+b \sin \left(c+d x^3\right)}{3 x^3}","-\frac{a}{3 x^3}+\frac{1}{3} b d \cos (c) \text{Ci}\left(d x^3\right)-\frac{1}{3} b d \sin (c) \text{Si}\left(d x^3\right)-\frac{b \sin \left(c+d x^3\right)}{3 x^3}",1,"-1/3*(a - b*d*x^3*Cos[c]*CosIntegral[d*x^3] + b*Sin[c + d*x^3] + b*d*x^3*Sin[c]*SinIntegral[d*x^3])/x^3","A",1
61,1,124,112,0.2362993,"\int x^4 \left(a+b \sin \left(c+d x^3\right)\right) \, dx","Integrate[x^4*(a + b*Sin[c + d*x^3]),x]","\frac{d x^8 \left(3 \left(d^2 x^6\right)^{2/3} \left(3 a d x^3-5 b \cos \left(c+d x^3\right)\right)-5 b \left(-i d x^3\right)^{2/3} (\cos (c)-i \sin (c)) \Gamma \left(\frac{2}{3},i d x^3\right)-5 b \left(i d x^3\right)^{2/3} (\cos (c)+i \sin (c)) \Gamma \left(\frac{2}{3},-i d x^3\right)\right)}{45 \left(d^2 x^6\right)^{5/3}}","\frac{a x^5}{5}-\frac{b x^2 \cos \left(c+d x^3\right)}{3 d}-\frac{b e^{i c} x^2 \Gamma \left(\frac{2}{3},-i d x^3\right)}{9 d \left(-i d x^3\right)^{2/3}}-\frac{b e^{-i c} x^2 \Gamma \left(\frac{2}{3},i d x^3\right)}{9 d \left(i d x^3\right)^{2/3}}",1,"(d*x^8*(3*(d^2*x^6)^(2/3)*(3*a*d*x^3 - 5*b*Cos[c + d*x^3]) - 5*b*((-I)*d*x^3)^(2/3)*Gamma[2/3, I*d*x^3]*(Cos[c] - I*Sin[c]) - 5*b*(I*d*x^3)^(2/3)*Gamma[2/3, (-I)*d*x^3]*(Cos[c] + I*Sin[c])))/(45*(d^2*x^6)^(5/3))","A",1
62,1,108,91,0.1277444,"\int x \left(a+b \sin \left(c+d x^3\right)\right) \, dx","Integrate[x*(a + b*Sin[c + d*x^3]),x]","\frac{x^2 \left(3 a \left(d^2 x^6\right)^{2/3}+b \left(-i d x^3\right)^{2/3} (-\sin (c)-i \cos (c)) \Gamma \left(\frac{2}{3},i d x^3\right)+i b \left(i d x^3\right)^{2/3} (\cos (c)+i \sin (c)) \Gamma \left(\frac{2}{3},-i d x^3\right)\right)}{6 \left(d^2 x^6\right)^{2/3}}","\frac{a x^2}{2}+\frac{i b e^{i c} x^2 \Gamma \left(\frac{2}{3},-i d x^3\right)}{6 \left(-i d x^3\right)^{2/3}}-\frac{i b e^{-i c} x^2 \Gamma \left(\frac{2}{3},i d x^3\right)}{6 \left(i d x^3\right)^{2/3}}",1,"(x^2*(3*a*(d^2*x^6)^(2/3) + b*((-I)*d*x^3)^(2/3)*Gamma[2/3, I*d*x^3]*((-I)*Cos[c] - Sin[c]) + I*b*(I*d*x^3)^(2/3)*Gamma[2/3, (-I)*d*x^3]*(Cos[c] + I*Sin[c])))/(6*(d^2*x^6)^(2/3))","A",1
63,1,120,101,0.2139554,"\int \frac{a+b \sin \left(c+d x^3\right)}{x^2} \, dx","Integrate[(a + b*Sin[c + d*x^3])/x^2,x]","\frac{-2 \left(d^2 x^6\right)^{2/3} \left(a+b \sin \left(c+d x^3\right)\right)-i b \left(-i d x^3\right)^{5/3} (\cos (c)-i \sin (c)) \Gamma \left(\frac{2}{3},i d x^3\right)+i b \left(i d x^3\right)^{5/3} (\cos (c)+i \sin (c)) \Gamma \left(\frac{2}{3},-i d x^3\right)}{2 x \left(d^2 x^6\right)^{2/3}}","-\frac{a}{x}-\frac{b \sin \left(c+d x^3\right)}{x}-\frac{b e^{i c} d x^2 \Gamma \left(\frac{2}{3},-i d x^3\right)}{2 \left(-i d x^3\right)^{2/3}}-\frac{b e^{-i c} d x^2 \Gamma \left(\frac{2}{3},i d x^3\right)}{2 \left(i d x^3\right)^{2/3}}",1,"((-I)*b*((-I)*d*x^3)^(5/3)*Gamma[2/3, I*d*x^3]*(Cos[c] - I*Sin[c]) + I*b*(I*d*x^3)^(5/3)*Gamma[2/3, (-I)*d*x^3]*(Cos[c] + I*Sin[c]) - 2*(d^2*x^6)^(2/3)*(a + b*Sin[c + d*x^3]))/(2*x*(d^2*x^6)^(2/3))","A",1
64,1,143,130,0.4044251,"\int \frac{a+b \sin \left(c+d x^3\right)}{x^5} \, dx","Integrate[(a + b*Sin[c + d*x^3])/x^5,x]","\frac{-2 \left(d^2 x^6\right)^{2/3} \left(a+b \sin \left(c+d x^3\right)+3 b d x^3 \cos \left(c+d x^3\right)\right)+3 b d^2 x^6 \left(i d x^3\right)^{2/3} (\sin (c)-i \cos (c)) \Gamma \left(\frac{2}{3},-i d x^3\right)+3 b d^2 x^6 \left(-i d x^3\right)^{2/3} (\sin (c)+i \cos (c)) \Gamma \left(\frac{2}{3},i d x^3\right)}{8 x^4 \left(d^2 x^6\right)^{2/3}}","-\frac{a}{4 x^4}-\frac{3 i b e^{i c} d^2 x^2 \Gamma \left(\frac{2}{3},-i d x^3\right)}{8 \left(-i d x^3\right)^{2/3}}+\frac{3 i b e^{-i c} d^2 x^2 \Gamma \left(\frac{2}{3},i d x^3\right)}{8 \left(i d x^3\right)^{2/3}}-\frac{3 b d \cos \left(c+d x^3\right)}{4 x}-\frac{b \sin \left(c+d x^3\right)}{4 x^4}",1,"(3*b*d^2*x^6*(I*d*x^3)^(2/3)*Gamma[2/3, (-I)*d*x^3]*((-I)*Cos[c] + Sin[c]) + 3*b*d^2*x^6*((-I)*d*x^3)^(2/3)*Gamma[2/3, I*d*x^3]*(I*Cos[c] + Sin[c]) - 2*(d^2*x^6)^(2/3)*(a + 3*b*d*x^3*Cos[c + d*x^3] + b*Sin[c + d*x^3]))/(8*x^4*(d^2*x^6)^(2/3))","A",1
65,1,124,106,0.1932518,"\int x^3 \left(a+b \sin \left(c+d x^3\right)\right) \, dx","Integrate[x^3*(a + b*Sin[c + d*x^3]),x]","\frac{d x^7 \left(3 \sqrt[3]{d^2 x^6} \left(3 a d x^3-4 b \cos \left(c+d x^3\right)\right)-2 b \sqrt[3]{-i d x^3} (\cos (c)-i \sin (c)) \Gamma \left(\frac{1}{3},i d x^3\right)-2 b \sqrt[3]{i d x^3} (\cos (c)+i \sin (c)) \Gamma \left(\frac{1}{3},-i d x^3\right)\right)}{36 \left(d^2 x^6\right)^{4/3}}","\frac{a x^4}{4}-\frac{b x \cos \left(c+d x^3\right)}{3 d}-\frac{b e^{i c} x \Gamma \left(\frac{1}{3},-i d x^3\right)}{18 d \sqrt[3]{-i d x^3}}-\frac{b e^{-i c} x \Gamma \left(\frac{1}{3},i d x^3\right)}{18 d \sqrt[3]{i d x^3}}",1,"(d*x^7*(3*(d^2*x^6)^(1/3)*(3*a*d*x^3 - 4*b*Cos[c + d*x^3]) - 2*b*((-I)*d*x^3)^(1/3)*Gamma[1/3, I*d*x^3]*(Cos[c] - I*Sin[c]) - 2*b*(I*d*x^3)^(1/3)*Gamma[1/3, (-I)*d*x^3]*(Cos[c] + I*Sin[c])))/(36*(d^2*x^6)^(4/3))","A",1
66,1,138,82,0.1008299,"\int \left(a+b \sin \left(c+d x^3\right)\right) \, dx","Integrate[a + b*Sin[c + d*x^3],x]","a x-\frac{1}{2} i b \cos (c) \left(\frac{x \Gamma \left(\frac{1}{3},i d x^3\right)}{3 \sqrt[3]{i d x^3}}-\frac{x \Gamma \left(\frac{1}{3},-i d x^3\right)}{3 \sqrt[3]{-i d x^3}}\right)+\frac{1}{2} b \sin (c) \left(-\frac{x \Gamma \left(\frac{1}{3},-i d x^3\right)}{3 \sqrt[3]{-i d x^3}}-\frac{x \Gamma \left(\frac{1}{3},i d x^3\right)}{3 \sqrt[3]{i d x^3}}\right)","a x+\frac{i b e^{i c} x \Gamma \left(\frac{1}{3},-i d x^3\right)}{6 \sqrt[3]{-i d x^3}}-\frac{i b e^{-i c} x \Gamma \left(\frac{1}{3},i d x^3\right)}{6 \sqrt[3]{i d x^3}}",1,"a*x - (I/2)*b*Cos[c]*(-1/3*(x*Gamma[1/3, (-I)*d*x^3])/((-I)*d*x^3)^(1/3) + (x*Gamma[1/3, I*d*x^3])/(3*(I*d*x^3)^(1/3))) + (b*(-1/3*(x*Gamma[1/3, (-I)*d*x^3])/((-I)*d*x^3)^(1/3) - (x*Gamma[1/3, I*d*x^3])/(3*(I*d*x^3)^(1/3)))*Sin[c])/2","A",1
67,1,120,101,0.1909015,"\int \frac{a+b \sin \left(c+d x^3\right)}{x^3} \, dx","Integrate[(a + b*Sin[c + d*x^3])/x^3,x]","\frac{-2 \sqrt[3]{d^2 x^6} \left(a+b \sin \left(c+d x^3\right)\right)-i b \left(-i d x^3\right)^{4/3} (\cos (c)-i \sin (c)) \Gamma \left(\frac{1}{3},i d x^3\right)+i b \left(i d x^3\right)^{4/3} (\cos (c)+i \sin (c)) \Gamma \left(\frac{1}{3},-i d x^3\right)}{4 x^2 \sqrt[3]{d^2 x^6}}","-\frac{a}{2 x^2}-\frac{b e^{i c} d x \Gamma \left(\frac{1}{3},-i d x^3\right)}{4 \sqrt[3]{-i d x^3}}-\frac{b e^{-i c} d x \Gamma \left(\frac{1}{3},i d x^3\right)}{4 \sqrt[3]{i d x^3}}-\frac{b \sin \left(c+d x^3\right)}{2 x^2}",1,"((-I)*b*((-I)*d*x^3)^(4/3)*Gamma[1/3, I*d*x^3]*(Cos[c] - I*Sin[c]) + I*b*(I*d*x^3)^(4/3)*Gamma[1/3, (-I)*d*x^3]*(Cos[c] + I*Sin[c]) - 2*(d^2*x^6)^(1/3)*(a + b*Sin[c + d*x^3]))/(4*x^2*(d^2*x^6)^(1/3))","A",1
68,1,146,126,0.4573519,"\int \frac{a+b \sin \left(c+d x^3\right)}{x^6} \, dx","Integrate[(a + b*Sin[c + d*x^3])/x^6,x]","\frac{-2 \sqrt[3]{d^2 x^6} \left(2 a+2 b \sin \left(c+d x^3\right)+3 b d x^3 \cos \left(c+d x^3\right)\right)+3 b d^2 x^6 \sqrt[3]{i d x^3} (\sin (c)-i \cos (c)) \Gamma \left(\frac{1}{3},-i d x^3\right)+3 b d^2 x^6 \sqrt[3]{-i d x^3} (\sin (c)+i \cos (c)) \Gamma \left(\frac{1}{3},i d x^3\right)}{20 x^5 \sqrt[3]{d^2 x^6}}","-\frac{a}{5 x^5}-\frac{3 i b e^{i c} d^2 x \Gamma \left(\frac{1}{3},-i d x^3\right)}{20 \sqrt[3]{-i d x^3}}+\frac{3 i b e^{-i c} d^2 x \Gamma \left(\frac{1}{3},i d x^3\right)}{20 \sqrt[3]{i d x^3}}-\frac{b \sin \left(c+d x^3\right)}{5 x^5}-\frac{3 b d \cos \left(c+d x^3\right)}{10 x^2}",1,"(3*b*d^2*x^6*(I*d*x^3)^(1/3)*Gamma[1/3, (-I)*d*x^3]*((-I)*Cos[c] + Sin[c]) + 3*b*d^2*x^6*((-I)*d*x^3)^(1/3)*Gamma[1/3, I*d*x^3]*(I*Cos[c] + Sin[c]) - 2*(d^2*x^6)^(1/3)*(2*a + 3*b*d*x^3*Cos[c + d*x^3] + 2*b*Sin[c + d*x^3]))/(20*x^5*(d^2*x^6)^(1/3))","A",1
69,1,92,107,0.2912182,"\int x^5 \left(a+b \sin \left(c+d x^3\right)\right)^2 \, dx","Integrate[x^5*(a + b*Sin[c + d*x^3])^2,x]","\frac{4 a^2 d^2 x^6+16 a b \sin \left(c+d x^3\right)-16 a b d x^3 \cos \left(c+d x^3\right)-2 b^2 d x^3 \sin \left(2 \left(c+d x^3\right)\right)-b^2 \cos \left(2 \left(c+d x^3\right)\right)+2 b^2 d^2 x^6}{24 d^2}","\frac{a^2 x^6}{6}+\frac{2 a b \sin \left(c+d x^3\right)}{3 d^2}-\frac{2 a b x^3 \cos \left(c+d x^3\right)}{3 d}+\frac{b^2 \sin ^2\left(c+d x^3\right)}{12 d^2}-\frac{b^2 x^3 \sin \left(c+d x^3\right) \cos \left(c+d x^3\right)}{6 d}+\frac{b^2 x^6}{12}",1,"(4*a^2*d^2*x^6 + 2*b^2*d^2*x^6 - 16*a*b*d*x^3*Cos[c + d*x^3] - b^2*Cos[2*(c + d*x^3)] + 16*a*b*Sin[c + d*x^3] - 2*b^2*d*x^3*Sin[2*(c + d*x^3)])/(24*d^2)","A",1
70,1,52,60,0.1555048,"\int x^2 \left(a+b \sin \left(c+d x^3\right)\right)^2 \, dx","Integrate[x^2*(a + b*Sin[c + d*x^3])^2,x]","-\frac{-2 \left(2 a^2+b^2\right) \left(c+d x^3\right)+8 a b \cos \left(c+d x^3\right)+b^2 \sin \left(2 \left(c+d x^3\right)\right)}{12 d}","\frac{1}{6} x^3 \left(2 a^2+b^2\right)-\frac{2 a b \cos \left(c+d x^3\right)}{3 d}-\frac{b^2 \sin \left(c+d x^3\right) \cos \left(c+d x^3\right)}{6 d}",1,"-1/12*(-2*(2*a^2 + b^2)*(c + d*x^3) + 8*a*b*Cos[c + d*x^3] + b^2*Sin[2*(c + d*x^3)])/d","A",1
71,1,71,80,0.1683201,"\int \frac{\left(a+b \sin \left(c+d x^3\right)\right)^2}{x} \, dx","Integrate[(a + b*Sin[c + d*x^3])^2/x,x]","\frac{1}{2} \left(2 a^2+b^2\right) \log (x)-\frac{1}{6} b \left(-4 a \sin (c) \text{Ci}\left(d x^3\right)-4 a \cos (c) \text{Si}\left(d x^3\right)+b \cos (2 c) \text{Ci}\left(2 d x^3\right)-b \sin (2 c) \text{Si}\left(2 d x^3\right)\right)","\frac{1}{2} \left(2 a^2+b^2\right) \log (x)+\frac{2}{3} a b \sin (c) \text{Ci}\left(d x^3\right)+\frac{2}{3} a b \cos (c) \text{Si}\left(d x^3\right)-\frac{1}{6} b^2 \cos (2 c) \text{Ci}\left(2 d x^3\right)+\frac{1}{6} b^2 \sin (2 c) \text{Si}\left(2 d x^3\right)",1,"((2*a^2 + b^2)*Log[x])/2 - (b*(b*Cos[2*c]*CosIntegral[2*d*x^3] - 4*a*CosIntegral[d*x^3]*Sin[c] - 4*a*Cos[c]*SinIntegral[d*x^3] - b*Sin[2*c]*SinIntegral[2*d*x^3]))/6","A",1
72,1,116,122,0.2745713,"\int \frac{\left(a+b \sin \left(c+d x^3\right)\right)^2}{x^4} \, dx","Integrate[(a + b*Sin[c + d*x^3])^2/x^4,x]","\frac{-2 a^2+4 a b d x^3 \cos (c) \text{Ci}\left(d x^3\right)-4 a b d x^3 \sin (c) \text{Si}\left(d x^3\right)-4 a b \sin \left(c+d x^3\right)+2 b^2 d x^3 \sin (2 c) \text{Ci}\left(2 d x^3\right)+2 b^2 d x^3 \cos (2 c) \text{Si}\left(2 d x^3\right)+b^2 \cos \left(2 \left(c+d x^3\right)\right)-b^2}{6 x^3}","-\frac{2 a^2+b^2}{6 x^3}+\frac{2}{3} a b d \cos (c) \text{Ci}\left(d x^3\right)-\frac{2}{3} a b d \sin (c) \text{Si}\left(d x^3\right)-\frac{2 a b \sin \left(c+d x^3\right)}{3 x^3}+\frac{1}{3} b^2 d \sin (2 c) \text{Ci}\left(2 d x^3\right)+\frac{1}{3} b^2 d \cos (2 c) \text{Si}\left(2 d x^3\right)+\frac{b^2 \cos \left(2 \left(c+d x^3\right)\right)}{6 x^3}",1,"(-2*a^2 - b^2 + b^2*Cos[2*(c + d*x^3)] + 4*a*b*d*x^3*Cos[c]*CosIntegral[d*x^3] + 2*b^2*d*x^3*CosIntegral[2*d*x^3]*Sin[2*c] - 4*a*b*Sin[c + d*x^3] - 4*a*b*d*x^3*Sin[c]*SinIntegral[d*x^3] + 2*b^2*d*x^3*Cos[2*c]*SinIntegral[2*d*x^3])/(6*x^3)","A",1
73,1,339,249,0.6302574,"\int x^4 \left(a+b \sin \left(c+d x^3\right)\right)^2 \, dx","Integrate[x^4*(a + b*Sin[c + d*x^3])^2,x]","\frac{d x^8 \left(72 a^2 d x^3 \left(d^2 x^6\right)^{2/3}-240 a b \left(d^2 x^6\right)^{2/3} \cos \left(c+d x^3\right)-80 a b \left(-i d x^3\right)^{2/3} (\cos (c)-i \sin (c)) \Gamma \left(\frac{2}{3},i d x^3\right)-80 a b \left(i d x^3\right)^{2/3} (\cos (c)+i \sin (c)) \Gamma \left(\frac{2}{3},-i d x^3\right)-30 b^2 \left(d^2 x^6\right)^{2/3} \sin \left(2 \left(c+d x^3\right)\right)+5 i \sqrt[3]{2} b^2 \cos (2 c) \left(i d x^3\right)^{2/3} \Gamma \left(\frac{2}{3},-2 i d x^3\right)-5 i \sqrt[3]{2} b^2 \cos (2 c) \left(-i d x^3\right)^{2/3} \Gamma \left(\frac{2}{3},2 i d x^3\right)-5 \sqrt[3]{2} b^2 \sin (2 c) \left(i d x^3\right)^{2/3} \Gamma \left(\frac{2}{3},-2 i d x^3\right)-5 \sqrt[3]{2} b^2 \sin (2 c) \left(-i d x^3\right)^{2/3} \Gamma \left(\frac{2}{3},2 i d x^3\right)+36 b^2 d x^3 \left(d^2 x^6\right)^{2/3}\right)}{360 \left(d^2 x^6\right)^{5/3}}","\frac{1}{10} x^5 \left(2 a^2+b^2\right)-\frac{2 a b x^2 \cos \left(c+d x^3\right)}{3 d}-\frac{2 a b e^{i c} x^2 \Gamma \left(\frac{2}{3},-i d x^3\right)}{9 d \left(-i d x^3\right)^{2/3}}-\frac{2 a b e^{-i c} x^2 \Gamma \left(\frac{2}{3},i d x^3\right)}{9 d \left(i d x^3\right)^{2/3}}-\frac{b^2 x^2 \sin \left(2 c+2 d x^3\right)}{12 d}+\frac{i b^2 e^{2 i c} x^2 \Gamma \left(\frac{2}{3},-2 i d x^3\right)}{36\ 2^{2/3} d \left(-i d x^3\right)^{2/3}}-\frac{i b^2 e^{-2 i c} x^2 \Gamma \left(\frac{2}{3},2 i d x^3\right)}{36\ 2^{2/3} d \left(i d x^3\right)^{2/3}}",1,"(d*x^8*(72*a^2*d*x^3*(d^2*x^6)^(2/3) + 36*b^2*d*x^3*(d^2*x^6)^(2/3) - 240*a*b*(d^2*x^6)^(2/3)*Cos[c + d*x^3] + (5*I)*2^(1/3)*b^2*(I*d*x^3)^(2/3)*Cos[2*c]*Gamma[2/3, (-2*I)*d*x^3] - (5*I)*2^(1/3)*b^2*((-I)*d*x^3)^(2/3)*Cos[2*c]*Gamma[2/3, (2*I)*d*x^3] - 80*a*b*((-I)*d*x^3)^(2/3)*Gamma[2/3, I*d*x^3]*(Cos[c] - I*Sin[c]) - 80*a*b*(I*d*x^3)^(2/3)*Gamma[2/3, (-I)*d*x^3]*(Cos[c] + I*Sin[c]) - 5*2^(1/3)*b^2*(I*d*x^3)^(2/3)*Gamma[2/3, (-2*I)*d*x^3]*Sin[2*c] - 5*2^(1/3)*b^2*((-I)*d*x^3)^(2/3)*Gamma[2/3, (2*I)*d*x^3]*Sin[2*c] - 30*b^2*(d^2*x^6)^(2/3)*Sin[2*(c + d*x^3)]))/(360*(d^2*x^6)^(5/3))","A",1
74,1,283,193,0.3644802,"\int x \left(a+b \sin \left(c+d x^3\right)\right)^2 \, dx","Integrate[x*(a + b*Sin[c + d*x^3])^2,x]","\frac{x^2 \left(12 a^2 \left(d^2 x^6\right)^{2/3}-8 i a b \left(-i d x^3\right)^{2/3} (\cos (c)-i \sin (c)) \Gamma \left(\frac{2}{3},i d x^3\right)+8 i a b \left(i d x^3\right)^{2/3} (\cos (c)+i \sin (c)) \Gamma \left(\frac{2}{3},-i d x^3\right)+\sqrt[3]{2} b^2 \cos (2 c) \left(i d x^3\right)^{2/3} \Gamma \left(\frac{2}{3},-2 i d x^3\right)+\sqrt[3]{2} b^2 \cos (2 c) \left(-i d x^3\right)^{2/3} \Gamma \left(\frac{2}{3},2 i d x^3\right)+i \sqrt[3]{2} b^2 \sin (2 c) \left(i d x^3\right)^{2/3} \Gamma \left(\frac{2}{3},-2 i d x^3\right)-i \sqrt[3]{2} b^2 \sin (2 c) \left(-i d x^3\right)^{2/3} \Gamma \left(\frac{2}{3},2 i d x^3\right)+6 b^2 \left(d^2 x^6\right)^{2/3}\right)}{24 \left(d^2 x^6\right)^{2/3}}","\frac{1}{4} x^2 \left(2 a^2+b^2\right)+\frac{i a b e^{i c} x^2 \Gamma \left(\frac{2}{3},-i d x^3\right)}{3 \left(-i d x^3\right)^{2/3}}-\frac{i a b e^{-i c} x^2 \Gamma \left(\frac{2}{3},i d x^3\right)}{3 \left(i d x^3\right)^{2/3}}+\frac{b^2 e^{2 i c} x^2 \Gamma \left(\frac{2}{3},-2 i d x^3\right)}{12\ 2^{2/3} \left(-i d x^3\right)^{2/3}}+\frac{b^2 e^{-2 i c} x^2 \Gamma \left(\frac{2}{3},2 i d x^3\right)}{12\ 2^{2/3} \left(i d x^3\right)^{2/3}}",1,"(x^2*(12*a^2*(d^2*x^6)^(2/3) + 6*b^2*(d^2*x^6)^(2/3) + 2^(1/3)*b^2*(I*d*x^3)^(2/3)*Cos[2*c]*Gamma[2/3, (-2*I)*d*x^3] + 2^(1/3)*b^2*((-I)*d*x^3)^(2/3)*Cos[2*c]*Gamma[2/3, (2*I)*d*x^3] - (8*I)*a*b*((-I)*d*x^3)^(2/3)*Gamma[2/3, I*d*x^3]*(Cos[c] - I*Sin[c]) + (8*I)*a*b*(I*d*x^3)^(2/3)*Gamma[2/3, (-I)*d*x^3]*(Cos[c] + I*Sin[c]) + I*2^(1/3)*b^2*(I*d*x^3)^(2/3)*Gamma[2/3, (-2*I)*d*x^3]*Sin[2*c] - I*2^(1/3)*b^2*((-I)*d*x^3)^(2/3)*Gamma[2/3, (2*I)*d*x^3]*Sin[2*c]))/(24*(d^2*x^6)^(2/3))","A",1
75,1,332,231,0.5912065,"\int \frac{\left(a+b \sin \left(c+d x^3\right)\right)^2}{x^2} \, dx","Integrate[(a + b*Sin[c + d*x^3])^2/x^2,x]","\frac{-4 a^2 \left(d^2 x^6\right)^{2/3}-8 a b \left(d^2 x^6\right)^{2/3} \sin \left(c+d x^3\right)-4 i a b \left(-i d x^3\right)^{5/3} (\cos (c)-i \sin (c)) \Gamma \left(\frac{2}{3},i d x^3\right)+4 i a b \left(i d x^3\right)^{5/3} (\cos (c)+i \sin (c)) \Gamma \left(\frac{2}{3},-i d x^3\right)+2 b^2 \left(d^2 x^6\right)^{2/3} \cos \left(2 \left(c+d x^3\right)\right)+\sqrt[3]{2} b^2 \cos (2 c) \left(i d x^3\right)^{5/3} \Gamma \left(\frac{2}{3},-2 i d x^3\right)+\sqrt[3]{2} b^2 \cos (2 c) \left(-i d x^3\right)^{5/3} \Gamma \left(\frac{2}{3},2 i d x^3\right)+i \sqrt[3]{2} b^2 \sin (2 c) \left(i d x^3\right)^{5/3} \Gamma \left(\frac{2}{3},-2 i d x^3\right)-i \sqrt[3]{2} b^2 \sin (2 c) \left(-i d x^3\right)^{5/3} \Gamma \left(\frac{2}{3},2 i d x^3\right)-2 b^2 \left(d^2 x^6\right)^{2/3}}{4 x \left(d^2 x^6\right)^{2/3}}","\frac{-2 a^2-b^2}{2 x}-\frac{2 a b \sin \left(c+d x^3\right)}{x}-\frac{a b e^{i c} d x^2 \Gamma \left(\frac{2}{3},-i d x^3\right)}{\left(-i d x^3\right)^{2/3}}-\frac{a b e^{-i c} d x^2 \Gamma \left(\frac{2}{3},i d x^3\right)}{\left(i d x^3\right)^{2/3}}+\frac{b^2 \cos \left(2 c+2 d x^3\right)}{2 x}+\frac{i b^2 e^{2 i c} d x^2 \Gamma \left(\frac{2}{3},-2 i d x^3\right)}{2\ 2^{2/3} \left(-i d x^3\right)^{2/3}}-\frac{i b^2 e^{-2 i c} d x^2 \Gamma \left(\frac{2}{3},2 i d x^3\right)}{2\ 2^{2/3} \left(i d x^3\right)^{2/3}}",1,"(-4*a^2*(d^2*x^6)^(2/3) - 2*b^2*(d^2*x^6)^(2/3) + 2*b^2*(d^2*x^6)^(2/3)*Cos[2*(c + d*x^3)] + 2^(1/3)*b^2*(I*d*x^3)^(5/3)*Cos[2*c]*Gamma[2/3, (-2*I)*d*x^3] + 2^(1/3)*b^2*((-I)*d*x^3)^(5/3)*Cos[2*c]*Gamma[2/3, (2*I)*d*x^3] - (4*I)*a*b*((-I)*d*x^3)^(5/3)*Gamma[2/3, I*d*x^3]*(Cos[c] - I*Sin[c]) + (4*I)*a*b*(I*d*x^3)^(5/3)*Gamma[2/3, (-I)*d*x^3]*(Cos[c] + I*Sin[c]) + I*2^(1/3)*b^2*(I*d*x^3)^(5/3)*Gamma[2/3, (-2*I)*d*x^3]*Sin[2*c] - I*2^(1/3)*b^2*((-I)*d*x^3)^(5/3)*Gamma[2/3, (2*I)*d*x^3]*Sin[2*c] - 8*a*b*(d^2*x^6)^(2/3)*Sin[c + d*x^3])/(4*x*(d^2*x^6)^(2/3))","A",1
76,1,292,285,2.5321614,"\int \frac{\left(a+b \sin \left(c+d x^3\right)\right)^2}{x^5} \, dx","Integrate[(a + b*Sin[c + d*x^3])^2/x^5,x]","-\frac{2 a^2+6 i a b \left(i d x^3\right)^{2/3} \sqrt[3]{d^2 x^6} (\cos (c)+i \sin (c)) \Gamma \left(\frac{2}{3},-i d x^3\right)+4 a b \sin \left(c+d x^3\right)+12 a b d x^3 \cos \left(c+d x^3\right)+6 i a b \left(i d x^3\right)^{4/3} (\cos (c)-i \sin (c)) \Gamma \left(\frac{2}{3},i d x^3\right)+6 b^2 d x^3 \sin \left(2 \left(c+d x^3\right)\right)-b^2 \cos \left(2 \left(c+d x^3\right)\right)-3 \sqrt[3]{2} b^2 \cos (2 c) \left(i d x^3\right)^{4/3} \Gamma \left(\frac{2}{3},2 i d x^3\right)+3 i \sqrt[3]{2} b^2 \sin (2 c) \left(i d x^3\right)^{4/3} \Gamma \left(\frac{2}{3},2 i d x^3\right)-3 \sqrt[3]{2} b^2 \left(-i d x^3\right)^{4/3} (\cos (2 c)+i \sin (2 c)) \Gamma \left(\frac{2}{3},-2 i d x^3\right)+b^2}{8 x^4}","\frac{-2 a^2-b^2}{8 x^4}-\frac{3 i a b e^{i c} d^2 x^2 \Gamma \left(\frac{2}{3},-i d x^3\right)}{4 \left(-i d x^3\right)^{2/3}}+\frac{3 i a b e^{-i c} d^2 x^2 \Gamma \left(\frac{2}{3},i d x^3\right)}{4 \left(i d x^3\right)^{2/3}}-\frac{3 a b d \cos \left(c+d x^3\right)}{2 x}-\frac{a b \sin \left(c+d x^3\right)}{2 x^4}-\frac{3 b^2 e^{2 i c} d^2 x^2 \Gamma \left(\frac{2}{3},-2 i d x^3\right)}{4\ 2^{2/3} \left(-i d x^3\right)^{2/3}}-\frac{3 b^2 e^{-2 i c} d^2 x^2 \Gamma \left(\frac{2}{3},2 i d x^3\right)}{4\ 2^{2/3} \left(i d x^3\right)^{2/3}}-\frac{3 b^2 d \sin \left(2 c+2 d x^3\right)}{4 x}+\frac{b^2 \cos \left(2 c+2 d x^3\right)}{8 x^4}",1,"-1/8*(2*a^2 + b^2 + 12*a*b*d*x^3*Cos[c + d*x^3] - b^2*Cos[2*(c + d*x^3)] - 3*2^(1/3)*b^2*(I*d*x^3)^(4/3)*Cos[2*c]*Gamma[2/3, (2*I)*d*x^3] + (6*I)*a*b*(I*d*x^3)^(4/3)*Gamma[2/3, I*d*x^3]*(Cos[c] - I*Sin[c]) + (6*I)*a*b*(I*d*x^3)^(2/3)*(d^2*x^6)^(1/3)*Gamma[2/3, (-I)*d*x^3]*(Cos[c] + I*Sin[c]) - 3*2^(1/3)*b^2*((-I)*d*x^3)^(4/3)*Gamma[2/3, (-2*I)*d*x^3]*(Cos[2*c] + I*Sin[2*c]) + (3*I)*2^(1/3)*b^2*(I*d*x^3)^(4/3)*Gamma[2/3, (2*I)*d*x^3]*Sin[2*c] + 4*a*b*Sin[c + d*x^3] + 6*b^2*d*x^3*Sin[2*(c + d*x^3)])/x^4","A",1
77,1,339,237,0.579488,"\int x^3 \left(a+b \sin \left(c+d x^3\right)\right)^2 \, dx","Integrate[x^3*(a + b*Sin[c + d*x^3])^2,x]","\frac{d x^7 \left(36 a^2 d x^3 \sqrt[3]{d^2 x^6}-96 a b \sqrt[3]{d^2 x^6} \cos \left(c+d x^3\right)-16 a b \sqrt[3]{-i d x^3} (\cos (c)-i \sin (c)) \Gamma \left(\frac{1}{3},i d x^3\right)-16 a b \sqrt[3]{i d x^3} (\cos (c)+i \sin (c)) \Gamma \left(\frac{1}{3},-i d x^3\right)-12 b^2 \sqrt[3]{d^2 x^6} \sin \left(2 \left(c+d x^3\right)\right)+i 2^{2/3} b^2 \cos (2 c) \sqrt[3]{i d x^3} \Gamma \left(\frac{1}{3},-2 i d x^3\right)-i 2^{2/3} b^2 \cos (2 c) \sqrt[3]{-i d x^3} \Gamma \left(\frac{1}{3},2 i d x^3\right)-2^{2/3} b^2 \sin (2 c) \sqrt[3]{i d x^3} \Gamma \left(\frac{1}{3},-2 i d x^3\right)-2^{2/3} b^2 \sin (2 c) \sqrt[3]{-i d x^3} \Gamma \left(\frac{1}{3},2 i d x^3\right)+18 b^2 d x^3 \sqrt[3]{d^2 x^6}\right)}{144 \left(d^2 x^6\right)^{4/3}}","\frac{1}{8} x^4 \left(2 a^2+b^2\right)-\frac{2 a b x \cos \left(c+d x^3\right)}{3 d}-\frac{a b e^{i c} x \Gamma \left(\frac{1}{3},-i d x^3\right)}{9 d \sqrt[3]{-i d x^3}}-\frac{a b e^{-i c} x \Gamma \left(\frac{1}{3},i d x^3\right)}{9 d \sqrt[3]{i d x^3}}-\frac{b^2 x \sin \left(2 c+2 d x^3\right)}{12 d}+\frac{i b^2 e^{2 i c} x \Gamma \left(\frac{1}{3},-2 i d x^3\right)}{72 \sqrt[3]{2} d \sqrt[3]{-i d x^3}}-\frac{i b^2 e^{-2 i c} x \Gamma \left(\frac{1}{3},2 i d x^3\right)}{72 \sqrt[3]{2} d \sqrt[3]{i d x^3}}",1,"(d*x^7*(36*a^2*d*x^3*(d^2*x^6)^(1/3) + 18*b^2*d*x^3*(d^2*x^6)^(1/3) - 96*a*b*(d^2*x^6)^(1/3)*Cos[c + d*x^3] + I*2^(2/3)*b^2*(I*d*x^3)^(1/3)*Cos[2*c]*Gamma[1/3, (-2*I)*d*x^3] - I*2^(2/3)*b^2*((-I)*d*x^3)^(1/3)*Cos[2*c]*Gamma[1/3, (2*I)*d*x^3] - 16*a*b*((-I)*d*x^3)^(1/3)*Gamma[1/3, I*d*x^3]*(Cos[c] - I*Sin[c]) - 16*a*b*(I*d*x^3)^(1/3)*Gamma[1/3, (-I)*d*x^3]*(Cos[c] + I*Sin[c]) - 2^(2/3)*b^2*(I*d*x^3)^(1/3)*Gamma[1/3, (-2*I)*d*x^3]*Sin[2*c] - 2^(2/3)*b^2*((-I)*d*x^3)^(1/3)*Gamma[1/3, (2*I)*d*x^3]*Sin[2*c] - 12*b^2*(d^2*x^6)^(1/3)*Sin[2*(c + d*x^3)]))/(144*(d^2*x^6)^(4/3))","A",1
78,1,281,183,0.2699516,"\int \left(a+b \sin \left(c+d x^3\right)\right)^2 \, dx","Integrate[(a + b*Sin[c + d*x^3])^2,x]","\frac{x \left(24 a^2 \sqrt[3]{d^2 x^6}-8 i a b \sqrt[3]{-i d x^3} (\cos (c)-i \sin (c)) \Gamma \left(\frac{1}{3},i d x^3\right)+8 i a b \sqrt[3]{i d x^3} (\cos (c)+i \sin (c)) \Gamma \left(\frac{1}{3},-i d x^3\right)+2^{2/3} b^2 \cos (2 c) \sqrt[3]{i d x^3} \Gamma \left(\frac{1}{3},-2 i d x^3\right)+2^{2/3} b^2 \cos (2 c) \sqrt[3]{-i d x^3} \Gamma \left(\frac{1}{3},2 i d x^3\right)+i 2^{2/3} b^2 \sin (2 c) \sqrt[3]{i d x^3} \Gamma \left(\frac{1}{3},-2 i d x^3\right)-i 2^{2/3} b^2 \sin (2 c) \sqrt[3]{-i d x^3} \Gamma \left(\frac{1}{3},2 i d x^3\right)+12 b^2 \sqrt[3]{d^2 x^6}\right)}{24 \sqrt[3]{d^2 x^6}}","\frac{1}{2} x \left(2 a^2+b^2\right)+\frac{i a b e^{i c} x \Gamma \left(\frac{1}{3},-i d x^3\right)}{3 \sqrt[3]{-i d x^3}}-\frac{i a b e^{-i c} x \Gamma \left(\frac{1}{3},i d x^3\right)}{3 \sqrt[3]{i d x^3}}+\frac{b^2 e^{2 i c} x \Gamma \left(\frac{1}{3},-2 i d x^3\right)}{12 \sqrt[3]{2} \sqrt[3]{-i d x^3}}+\frac{b^2 e^{-2 i c} x \Gamma \left(\frac{1}{3},2 i d x^3\right)}{12 \sqrt[3]{2} \sqrt[3]{i d x^3}}",1,"(x*(24*a^2*(d^2*x^6)^(1/3) + 12*b^2*(d^2*x^6)^(1/3) + 2^(2/3)*b^2*(I*d*x^3)^(1/3)*Cos[2*c]*Gamma[1/3, (-2*I)*d*x^3] + 2^(2/3)*b^2*((-I)*d*x^3)^(1/3)*Cos[2*c]*Gamma[1/3, (2*I)*d*x^3] - (8*I)*a*b*((-I)*d*x^3)^(1/3)*Gamma[1/3, I*d*x^3]*(Cos[c] - I*Sin[c]) + (8*I)*a*b*(I*d*x^3)^(1/3)*Gamma[1/3, (-I)*d*x^3]*(Cos[c] + I*Sin[c]) + I*2^(2/3)*b^2*(I*d*x^3)^(1/3)*Gamma[1/3, (-2*I)*d*x^3]*Sin[2*c] - I*2^(2/3)*b^2*((-I)*d*x^3)^(1/3)*Gamma[1/3, (2*I)*d*x^3]*Sin[2*c]))/(24*(d^2*x^6)^(1/3))","A",1
79,1,332,227,0.5562849,"\int \frac{\left(a+b \sin \left(c+d x^3\right)\right)^2}{x^3} \, dx","Integrate[(a + b*Sin[c + d*x^3])^2/x^3,x]","\frac{-4 a^2 \sqrt[3]{d^2 x^6}-8 a b \sqrt[3]{d^2 x^6} \sin \left(c+d x^3\right)-4 i a b \left(-i d x^3\right)^{4/3} (\cos (c)-i \sin (c)) \Gamma \left(\frac{1}{3},i d x^3\right)+4 i a b \left(i d x^3\right)^{4/3} (\cos (c)+i \sin (c)) \Gamma \left(\frac{1}{3},-i d x^3\right)+2 b^2 \sqrt[3]{d^2 x^6} \cos \left(2 \left(c+d x^3\right)\right)+2^{2/3} b^2 \cos (2 c) \left(i d x^3\right)^{4/3} \Gamma \left(\frac{1}{3},-2 i d x^3\right)+2^{2/3} b^2 \cos (2 c) \left(-i d x^3\right)^{4/3} \Gamma \left(\frac{1}{3},2 i d x^3\right)+i 2^{2/3} b^2 \sin (2 c) \left(i d x^3\right)^{4/3} \Gamma \left(\frac{1}{3},-2 i d x^3\right)-i 2^{2/3} b^2 \sin (2 c) \left(-i d x^3\right)^{4/3} \Gamma \left(\frac{1}{3},2 i d x^3\right)-2 b^2 \sqrt[3]{d^2 x^6}}{8 x^2 \sqrt[3]{d^2 x^6}}","\frac{-2 a^2-b^2}{4 x^2}-\frac{a b e^{i c} d x \Gamma \left(\frac{1}{3},-i d x^3\right)}{2 \sqrt[3]{-i d x^3}}-\frac{a b e^{-i c} d x \Gamma \left(\frac{1}{3},i d x^3\right)}{2 \sqrt[3]{i d x^3}}-\frac{a b \sin \left(c+d x^3\right)}{x^2}+\frac{i b^2 e^{2 i c} d x \Gamma \left(\frac{1}{3},-2 i d x^3\right)}{4 \sqrt[3]{2} \sqrt[3]{-i d x^3}}-\frac{i b^2 e^{-2 i c} d x \Gamma \left(\frac{1}{3},2 i d x^3\right)}{4 \sqrt[3]{2} \sqrt[3]{i d x^3}}+\frac{b^2 \cos \left(2 c+2 d x^3\right)}{4 x^2}",1,"(-4*a^2*(d^2*x^6)^(1/3) - 2*b^2*(d^2*x^6)^(1/3) + 2*b^2*(d^2*x^6)^(1/3)*Cos[2*(c + d*x^3)] + 2^(2/3)*b^2*(I*d*x^3)^(4/3)*Cos[2*c]*Gamma[1/3, (-2*I)*d*x^3] + 2^(2/3)*b^2*((-I)*d*x^3)^(4/3)*Cos[2*c]*Gamma[1/3, (2*I)*d*x^3] - (4*I)*a*b*((-I)*d*x^3)^(4/3)*Gamma[1/3, I*d*x^3]*(Cos[c] - I*Sin[c]) + (4*I)*a*b*(I*d*x^3)^(4/3)*Gamma[1/3, (-I)*d*x^3]*(Cos[c] + I*Sin[c]) + I*2^(2/3)*b^2*(I*d*x^3)^(4/3)*Gamma[1/3, (-2*I)*d*x^3]*Sin[2*c] - I*2^(2/3)*b^2*((-I)*d*x^3)^(4/3)*Gamma[1/3, (2*I)*d*x^3]*Sin[2*c] - 8*a*b*(d^2*x^6)^(1/3)*Sin[c + d*x^3])/(8*x^2*(d^2*x^6)^(1/3))","A",1
80,1,294,277,2.4574861,"\int \frac{\left(a+b \sin \left(c+d x^3\right)\right)^2}{x^6} \, dx","Integrate[(a + b*Sin[c + d*x^3])^2/x^6,x]","-\frac{4 a^2+6 i a b \sqrt[3]{i d x^3} \left(d^2 x^6\right)^{2/3} (\cos (c)+i \sin (c)) \Gamma \left(\frac{1}{3},-i d x^3\right)+8 a b \sin \left(c+d x^3\right)+12 a b d x^3 \cos \left(c+d x^3\right)+6 i a b \left(i d x^3\right)^{5/3} (\cos (c)-i \sin (c)) \Gamma \left(\frac{1}{3},i d x^3\right)+6 b^2 d x^3 \sin \left(2 \left(c+d x^3\right)\right)-2 b^2 \cos \left(2 \left(c+d x^3\right)\right)-3\ 2^{2/3} b^2 \cos (2 c) \left(i d x^3\right)^{5/3} \Gamma \left(\frac{1}{3},2 i d x^3\right)+3 i 2^{2/3} b^2 \sin (2 c) \left(i d x^3\right)^{5/3} \Gamma \left(\frac{1}{3},2 i d x^3\right)-3\ 2^{2/3} b^2 \left(-i d x^3\right)^{5/3} (\cos (2 c)+i \sin (2 c)) \Gamma \left(\frac{1}{3},-2 i d x^3\right)+2 b^2}{20 x^5}","\frac{-2 a^2-b^2}{10 x^5}-\frac{3 i a b e^{i c} d^2 x \Gamma \left(\frac{1}{3},-i d x^3\right)}{10 \sqrt[3]{-i d x^3}}+\frac{3 i a b e^{-i c} d^2 x \Gamma \left(\frac{1}{3},i d x^3\right)}{10 \sqrt[3]{i d x^3}}-\frac{2 a b \sin \left(c+d x^3\right)}{5 x^5}-\frac{3 a b d \cos \left(c+d x^3\right)}{5 x^2}-\frac{3 b^2 e^{2 i c} d^2 x \Gamma \left(\frac{1}{3},-2 i d x^3\right)}{10 \sqrt[3]{2} \sqrt[3]{-i d x^3}}-\frac{3 b^2 e^{-2 i c} d^2 x \Gamma \left(\frac{1}{3},2 i d x^3\right)}{10 \sqrt[3]{2} \sqrt[3]{i d x^3}}+\frac{b^2 \cos \left(2 c+2 d x^3\right)}{10 x^5}-\frac{3 b^2 d \sin \left(2 c+2 d x^3\right)}{10 x^2}",1,"-1/20*(4*a^2 + 2*b^2 + 12*a*b*d*x^3*Cos[c + d*x^3] - 2*b^2*Cos[2*(c + d*x^3)] - 3*2^(2/3)*b^2*(I*d*x^3)^(5/3)*Cos[2*c]*Gamma[1/3, (2*I)*d*x^3] + (6*I)*a*b*(I*d*x^3)^(5/3)*Gamma[1/3, I*d*x^3]*(Cos[c] - I*Sin[c]) + (6*I)*a*b*(I*d*x^3)^(1/3)*(d^2*x^6)^(2/3)*Gamma[1/3, (-I)*d*x^3]*(Cos[c] + I*Sin[c]) - 3*2^(2/3)*b^2*((-I)*d*x^3)^(5/3)*Gamma[1/3, (-2*I)*d*x^3]*(Cos[2*c] + I*Sin[2*c]) + (3*I)*2^(2/3)*b^2*(I*d*x^3)^(5/3)*Gamma[1/3, (2*I)*d*x^3]*Sin[2*c] + 8*a*b*Sin[c + d*x^3] + 6*b^2*d*x^3*Sin[2*(c + d*x^3)])/x^5","A",1
81,1,188,245,0.1670434,"\int \frac{x^5}{a+b \sin \left(c+d x^3\right)} \, dx","Integrate[x^5/(a + b*Sin[c + d*x^3]),x]","\frac{-\text{Li}_2\left(-\frac{i b e^{i \left(d x^3+c\right)}}{\sqrt{a^2-b^2}-a}\right)+\text{Li}_2\left(\frac{i b e^{i \left(d x^3+c\right)}}{a+\sqrt{a^2-b^2}}\right)-i d x^3 \left(\log \left(1+\frac{i b e^{i \left(c+d x^3\right)}}{\sqrt{a^2-b^2}-a}\right)-\log \left(1-\frac{i b e^{i \left(c+d x^3\right)}}{\sqrt{a^2-b^2}+a}\right)\right)}{3 d^2 \sqrt{a^2-b^2}}","-\frac{\text{Li}_2\left(\frac{i b e^{i \left(d x^3+c\right)}}{a-\sqrt{a^2-b^2}}\right)}{3 d^2 \sqrt{a^2-b^2}}+\frac{\text{Li}_2\left(\frac{i b e^{i \left(d x^3+c\right)}}{a+\sqrt{a^2-b^2}}\right)}{3 d^2 \sqrt{a^2-b^2}}-\frac{i x^3 \log \left(1-\frac{i b e^{i \left(c+d x^3\right)}}{a-\sqrt{a^2-b^2}}\right)}{3 d \sqrt{a^2-b^2}}+\frac{i x^3 \log \left(1-\frac{i b e^{i \left(c+d x^3\right)}}{\sqrt{a^2-b^2}+a}\right)}{3 d \sqrt{a^2-b^2}}",1,"((-I)*d*x^3*(Log[1 + (I*b*E^(I*(c + d*x^3)))/(-a + Sqrt[a^2 - b^2])] - Log[1 - (I*b*E^(I*(c + d*x^3)))/(a + Sqrt[a^2 - b^2])]) - PolyLog[2, ((-I)*b*E^(I*(c + d*x^3)))/(-a + Sqrt[a^2 - b^2])] + PolyLog[2, (I*b*E^(I*(c + d*x^3)))/(a + Sqrt[a^2 - b^2])])/(3*Sqrt[a^2 - b^2]*d^2)","A",1
82,1,51,51,0.1184606,"\int \frac{x^2}{a+b \sin \left(c+d x^3\right)} \, dx","Integrate[x^2/(a + b*Sin[c + d*x^3]),x]","\frac{2 \tan ^{-1}\left(\frac{a \tan \left(\frac{1}{2} \left(c+d x^3\right)\right)+b}{\sqrt{a^2-b^2}}\right)}{3 d \sqrt{a^2-b^2}}","\frac{2 \tan ^{-1}\left(\frac{a \tan \left(\frac{1}{2} \left(c+d x^3\right)\right)+b}{\sqrt{a^2-b^2}}\right)}{3 d \sqrt{a^2-b^2}}",1,"(2*ArcTan[(b + a*Tan[(c + d*x^3)/2])/Sqrt[a^2 - b^2]])/(3*Sqrt[a^2 - b^2]*d)","A",1
83,0,0,21,0.4367247,"\int \frac{1}{x \left(a+b \sin \left(c+d x^3\right)\right)} \, dx","Integrate[1/(x*(a + b*Sin[c + d*x^3])),x]","\int \frac{1}{x \left(a+b \sin \left(c+d x^3\right)\right)} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \sin \left(c+d x^3\right)\right)},x\right)",0,"Integrate[1/(x*(a + b*Sin[c + d*x^3])), x]","A",-1
84,0,0,21,0.4587624,"\int \frac{1}{x^4 \left(a+b \sin \left(c+d x^3\right)\right)} \, dx","Integrate[1/(x^4*(a + b*Sin[c + d*x^3])),x]","\int \frac{1}{x^4 \left(a+b \sin \left(c+d x^3\right)\right)} \, dx","\text{Int}\left(\frac{1}{x^4 \left(a+b \sin \left(c+d x^3\right)\right)},x\right)",0,"Integrate[1/(x^4*(a + b*Sin[c + d*x^3])), x]","A",-1
85,0,0,19,0.6094134,"\int \frac{x}{a+b \sin \left(c+d x^3\right)} \, dx","Integrate[x/(a + b*Sin[c + d*x^3]),x]","\int \frac{x}{a+b \sin \left(c+d x^3\right)} \, dx","\text{Int}\left(\frac{x}{a+b \sin \left(c+d x^3\right)},x\right)",0,"Integrate[x/(a + b*Sin[c + d*x^3]), x]","A",-1
86,0,0,21,0.3251447,"\int \frac{1}{x^2 \left(a+b \sin \left(c+d x^3\right)\right)} \, dx","Integrate[1/(x^2*(a + b*Sin[c + d*x^3])),x]","\int \frac{1}{x^2 \left(a+b \sin \left(c+d x^3\right)\right)} \, dx","\text{Int}\left(\frac{1}{x^2 \left(a+b \sin \left(c+d x^3\right)\right)},x\right)",0,"Integrate[1/(x^2*(a + b*Sin[c + d*x^3])), x]","A",-1
87,0,0,17,0.0249891,"\int \frac{1}{a+b \sin \left(c+d x^3\right)} \, dx","Integrate[(a + b*Sin[c + d*x^3])^(-1),x]","\int \frac{1}{a+b \sin \left(c+d x^3\right)} \, dx","\text{Int}\left(\frac{1}{a+b \sin \left(c+d x^3\right)},x\right)",0,"Integrate[(a + b*Sin[c + d*x^3])^(-1), x]","A",-1
88,0,0,21,0.3736953,"\int \frac{1}{x^3 \left(a+b \sin \left(c+d x^3\right)\right)} \, dx","Integrate[1/(x^3*(a + b*Sin[c + d*x^3])),x]","\int \frac{1}{x^3 \left(a+b \sin \left(c+d x^3\right)\right)} \, dx","\text{Int}\left(\frac{1}{x^3 \left(a+b \sin \left(c+d x^3\right)\right)},x\right)",0,"Integrate[1/(x^3*(a + b*Sin[c + d*x^3])), x]","A",-1
89,1,302,324,0.9842902,"\int \frac{x^5}{\left(a+b \sin \left(c+d x^3\right)\right)^2} \, dx","Integrate[x^5/(a + b*Sin[c + d*x^3])^2,x]","\frac{-\frac{a \text{Li}_2\left(-\frac{i b e^{i \left(d x^3+c\right)}}{\sqrt{a^2-b^2}-a}\right)}{\left(a^2-b^2\right)^{3/2}}+\frac{a \text{Li}_2\left(\frac{i b e^{i \left(d x^3+c\right)}}{a+\sqrt{a^2-b^2}}\right)}{\left(a^2-b^2\right)^{3/2}}-\frac{i a d x^3 \log \left(1+\frac{i b e^{i \left(c+d x^3\right)}}{\sqrt{a^2-b^2}-a}\right)}{\left(a^2-b^2\right)^{3/2}}+\frac{i a d x^3 \log \left(1-\frac{i b e^{i \left(c+d x^3\right)}}{\sqrt{a^2-b^2}+a}\right)}{\left(a^2-b^2\right)^{3/2}}-\frac{\log \left(a+b \sin \left(c+d x^3\right)\right)}{a^2-b^2}+\frac{b d x^3 \cos \left(c+d x^3\right)}{\left(a^2-b^2\right) \left(a+b \sin \left(c+d x^3\right)\right)}}{3 d^2}","-\frac{a \text{Li}_2\left(\frac{i b e^{i \left(d x^3+c\right)}}{a-\sqrt{a^2-b^2}}\right)}{3 d^2 \left(a^2-b^2\right)^{3/2}}+\frac{a \text{Li}_2\left(\frac{i b e^{i \left(d x^3+c\right)}}{a+\sqrt{a^2-b^2}}\right)}{3 d^2 \left(a^2-b^2\right)^{3/2}}-\frac{\log \left(a+b \sin \left(c+d x^3\right)\right)}{3 d^2 \left(a^2-b^2\right)}-\frac{i a x^3 \log \left(1-\frac{i b e^{i \left(c+d x^3\right)}}{a-\sqrt{a^2-b^2}}\right)}{3 d \left(a^2-b^2\right)^{3/2}}+\frac{i a x^3 \log \left(1-\frac{i b e^{i \left(c+d x^3\right)}}{\sqrt{a^2-b^2}+a}\right)}{3 d \left(a^2-b^2\right)^{3/2}}+\frac{b x^3 \cos \left(c+d x^3\right)}{3 d \left(a^2-b^2\right) \left(a+b \sin \left(c+d x^3\right)\right)}",1,"(((-I)*a*d*x^3*Log[1 + (I*b*E^(I*(c + d*x^3)))/(-a + Sqrt[a^2 - b^2])])/(a^2 - b^2)^(3/2) + (I*a*d*x^3*Log[1 - (I*b*E^(I*(c + d*x^3)))/(a + Sqrt[a^2 - b^2])])/(a^2 - b^2)^(3/2) - Log[a + b*Sin[c + d*x^3]]/(a^2 - b^2) - (a*PolyLog[2, ((-I)*b*E^(I*(c + d*x^3)))/(-a + Sqrt[a^2 - b^2])])/(a^2 - b^2)^(3/2) + (a*PolyLog[2, (I*b*E^(I*(c + d*x^3)))/(a + Sqrt[a^2 - b^2])])/(a^2 - b^2)^(3/2) + (b*d*x^3*Cos[c + d*x^3])/((a^2 - b^2)*(a + b*Sin[c + d*x^3])))/(3*d^2)","A",1
90,1,91,94,0.2067174,"\int \frac{x^2}{\left(a+b \sin \left(c+d x^3\right)\right)^2} \, dx","Integrate[x^2/(a + b*Sin[c + d*x^3])^2,x]","\frac{\frac{2 a \tan ^{-1}\left(\frac{a \tan \left(\frac{1}{2} \left(c+d x^3\right)\right)+b}{\sqrt{a^2-b^2}}\right)}{\sqrt{a^2-b^2}}+\frac{b \cos \left(c+d x^3\right)}{a+b \sin \left(c+d x^3\right)}}{3 d (a-b) (a+b)}","\frac{2 a \tan ^{-1}\left(\frac{a \tan \left(\frac{1}{2} \left(c+d x^3\right)\right)+b}{\sqrt{a^2-b^2}}\right)}{3 d \left(a^2-b^2\right)^{3/2}}+\frac{b \cos \left(c+d x^3\right)}{3 d \left(a^2-b^2\right) \left(a+b \sin \left(c+d x^3\right)\right)}",1,"((2*a*ArcTan[(b + a*Tan[(c + d*x^3)/2])/Sqrt[a^2 - b^2]])/Sqrt[a^2 - b^2] + (b*Cos[c + d*x^3])/(a + b*Sin[c + d*x^3]))/(3*(a - b)*(a + b)*d)","A",1
91,0,0,21,11.0418259,"\int \frac{1}{x \left(a+b \sin \left(c+d x^3\right)\right)^2} \, dx","Integrate[1/(x*(a + b*Sin[c + d*x^3])^2),x]","\int \frac{1}{x \left(a+b \sin \left(c+d x^3\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \sin \left(c+d x^3\right)\right)^2},x\right)",0,"Integrate[1/(x*(a + b*Sin[c + d*x^3])^2), x]","A",-1
92,0,0,21,13.3722772,"\int \frac{1}{x^4 \left(a+b \sin \left(c+d x^3\right)\right)^2} \, dx","Integrate[1/(x^4*(a + b*Sin[c + d*x^3])^2),x]","\int \frac{1}{x^4 \left(a+b \sin \left(c+d x^3\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x^4 \left(a+b \sin \left(c+d x^3\right)\right)^2},x\right)",0,"Integrate[1/(x^4*(a + b*Sin[c + d*x^3])^2), x]","A",-1
93,0,0,19,7.3155394,"\int \frac{x}{\left(a+b \sin \left(c+d x^3\right)\right)^2} \, dx","Integrate[x/(a + b*Sin[c + d*x^3])^2,x]","\int \frac{x}{\left(a+b \sin \left(c+d x^3\right)\right)^2} \, dx","\text{Int}\left(\frac{x}{\left(a+b \sin \left(c+d x^3\right)\right)^2},x\right)",0,"Integrate[x/(a + b*Sin[c + d*x^3])^2, x]","A",-1
94,0,0,21,11.6826877,"\int \frac{1}{x^2 \left(a+b \sin \left(c+d x^3\right)\right)^2} \, dx","Integrate[1/(x^2*(a + b*Sin[c + d*x^3])^2),x]","\int \frac{1}{x^2 \left(a+b \sin \left(c+d x^3\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x^2 \left(a+b \sin \left(c+d x^3\right)\right)^2},x\right)",0,"Integrate[1/(x^2*(a + b*Sin[c + d*x^3])^2), x]","A",-1
95,0,0,17,9.1252567,"\int \frac{1}{\left(a+b \sin \left(c+d x^3\right)\right)^2} \, dx","Integrate[(a + b*Sin[c + d*x^3])^(-2),x]","\int \frac{1}{\left(a+b \sin \left(c+d x^3\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{\left(a+b \sin \left(c+d x^3\right)\right)^2},x\right)",0,"Integrate[(a + b*Sin[c + d*x^3])^(-2), x]","A",-1
96,0,0,21,12.8298349,"\int \frac{1}{x^3 \left(a+b \sin \left(c+d x^3\right)\right)^2} \, dx","Integrate[1/(x^3*(a + b*Sin[c + d*x^3])^2),x]","\int \frac{1}{x^3 \left(a+b \sin \left(c+d x^3\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x^3 \left(a+b \sin \left(c+d x^3\right)\right)^2},x\right)",0,"Integrate[1/(x^3*(a + b*Sin[c + d*x^3])^2), x]","A",-1
97,0,0,23,0.8788104,"\int (e x)^m \left(a+b \sin \left(c+d x^3\right)\right)^p \, dx","Integrate[(e*x)^m*(a + b*Sin[c + d*x^3])^p,x]","\int (e x)^m \left(a+b \sin \left(c+d x^3\right)\right)^p \, dx","\text{Int}\left((e x)^m \left(a+b \sin \left(c+d x^3\right)\right)^p,x\right)",0,"Integrate[(e*x)^m*(a + b*Sin[c + d*x^3])^p, x]","A",-1
98,1,373,442,12.0163049,"\int (e x)^m \left(a+b \sin \left(c+d x^3\right)\right)^3 \, dx","Integrate[(e*x)^m*(a + b*Sin[c + d*x^3])^3,x]","\frac{1}{24} i x (e x)^m \left(3 b e^{i c} \left(4 a^2+b^2\right) \left(-i d x^3\right)^{-\frac{m}{3}-\frac{1}{3}} \Gamma \left(\frac{m+1}{3},-i d x^3\right)-3 b e^{-i c} \left(4 a^2+b^2\right) \left(i d x^3\right)^{-\frac{m}{3}-\frac{1}{3}} \Gamma \left(\frac{m+1}{3},i d x^3\right)-\frac{12 i a \left(2 a^2+3 b^2\right)}{m+1}-3 i a b^2 e^{2 i c} 2^{\frac{2}{3}-\frac{m}{3}} \left(-i d x^3\right)^{-\frac{m}{3}-\frac{1}{3}} \Gamma \left(\frac{m+1}{3},-2 i d x^3\right)-3 i a b^2 e^{-2 i c} 2^{\frac{2}{3}-\frac{m}{3}} \left(i d x^3\right)^{-\frac{m}{3}-\frac{1}{3}} \Gamma \left(\frac{m+1}{3},2 i d x^3\right)-b^3 e^{3 i c} 3^{-\frac{m}{3}-\frac{1}{3}} \left(-i d x^3\right)^{-\frac{m}{3}-\frac{1}{3}} \Gamma \left(\frac{m+1}{3},-3 i d x^3\right)+b^3 e^{-3 i c} 3^{-\frac{m}{3}-\frac{1}{3}} \left(i d x^3\right)^{-\frac{m}{3}-\frac{1}{3}} \Gamma \left(\frac{m+1}{3},3 i d x^3\right)\right)","\frac{i b e^{i c} \left(4 a^2+b^2\right) \left(-i d x^3\right)^{\frac{1}{3} (-m-1)} (e x)^{m+1} \Gamma \left(\frac{m+1}{3},-i d x^3\right)}{8 e}-\frac{i b e^{-i c} \left(4 a^2+b^2\right) \left(i d x^3\right)^{\frac{1}{3} (-m-1)} (e x)^{m+1} \Gamma \left(\frac{m+1}{3},i d x^3\right)}{8 e}+\frac{a \left(2 a^2+3 b^2\right) (e x)^{m+1}}{2 e (m+1)}+\frac{a b^2 e^{2 i c} 2^{-\frac{m}{3}-\frac{7}{3}} \left(-i d x^3\right)^{\frac{1}{3} (-m-1)} (e x)^{m+1} \Gamma \left(\frac{m+1}{3},-2 i d x^3\right)}{e}+\frac{a b^2 e^{-2 i c} 2^{-\frac{m}{3}-\frac{7}{3}} \left(i d x^3\right)^{\frac{1}{3} (-m-1)} (e x)^{m+1} \Gamma \left(\frac{m+1}{3},2 i d x^3\right)}{e}-\frac{i b^3 e^{3 i c} 3^{-\frac{m}{3}-\frac{4}{3}} \left(-i d x^3\right)^{\frac{1}{3} (-m-1)} (e x)^{m+1} \Gamma \left(\frac{m+1}{3},-3 i d x^3\right)}{8 e}+\frac{i b^3 e^{-3 i c} 3^{-\frac{m}{3}-\frac{4}{3}} \left(i d x^3\right)^{\frac{1}{3} (-m-1)} (e x)^{m+1} \Gamma \left(\frac{m+1}{3},3 i d x^3\right)}{8 e}",1,"(I/24)*x*(e*x)^m*(((-12*I)*a*(2*a^2 + 3*b^2))/(1 + m) + 3*b*(4*a^2 + b^2)*E^(I*c)*((-I)*d*x^3)^(-1/3 - m/3)*Gamma[(1 + m)/3, (-I)*d*x^3] - (3*b*(4*a^2 + b^2)*(I*d*x^3)^(-1/3 - m/3)*Gamma[(1 + m)/3, I*d*x^3])/E^(I*c) - (3*I)*2^(2/3 - m/3)*a*b^2*E^((2*I)*c)*((-I)*d*x^3)^(-1/3 - m/3)*Gamma[(1 + m)/3, (-2*I)*d*x^3] - ((3*I)*2^(2/3 - m/3)*a*b^2*(I*d*x^3)^(-1/3 - m/3)*Gamma[(1 + m)/3, (2*I)*d*x^3])/E^((2*I)*c) - 3^(-1/3 - m/3)*b^3*E^((3*I)*c)*((-I)*d*x^3)^(-1/3 - m/3)*Gamma[(1 + m)/3, (-3*I)*d*x^3] + (3^(-1/3 - m/3)*b^3*(I*d*x^3)^(-1/3 - m/3)*Gamma[(1 + m)/3, (3*I)*d*x^3])/E^((3*I)*c))","A",1
99,1,556,285,6.6720676,"\int (e x)^m \left(a+b \sin \left(c+d x^3\right)\right)^2 \, dx","Integrate[(e*x)^m*(a + b*Sin[c + d*x^3])^2,x]","\frac{2^{\frac{1}{3} (-m-7)} x \left(d^2 x^6\right)^{\frac{1}{3} (-m-1)} (e x)^m \left(3 a^2 2^{\frac{m+7}{3}} \left(d^2 x^6\right)^{\frac{m+1}{3}}-i a b 2^{\frac{m+7}{3}} (m+1) (\cos (c)-i \sin (c)) \left(-i d x^3\right)^{\frac{m+1}{3}} \Gamma \left(\frac{m+1}{3},i d x^3\right)+i a b 2^{\frac{m+7}{3}} (m+1) (\cos (c)+i \sin (c)) \left(i d x^3\right)^{\frac{m+1}{3}} \Gamma \left(\frac{m+1}{3},-i d x^3\right)+b^2 \cos (2 c) \left(-i d x^3\right)^{\frac{m+1}{3}} \Gamma \left(\frac{m+1}{3},2 i d x^3\right)+b^2 m \cos (2 c) \left(-i d x^3\right)^{\frac{m+1}{3}} \Gamma \left(\frac{m+1}{3},2 i d x^3\right)+b^2 \cos (2 c) \left(i d x^3\right)^{\frac{m+1}{3}} \Gamma \left(\frac{m+1}{3},-2 i d x^3\right)+b^2 m \cos (2 c) \left(i d x^3\right)^{\frac{m+1}{3}} \Gamma \left(\frac{m+1}{3},-2 i d x^3\right)-i b^2 \sin (2 c) \left(-i d x^3\right)^{\frac{m+1}{3}} \Gamma \left(\frac{m+1}{3},2 i d x^3\right)-i b^2 m \sin (2 c) \left(-i d x^3\right)^{\frac{m+1}{3}} \Gamma \left(\frac{m+1}{3},2 i d x^3\right)+i b^2 \sin (2 c) \left(i d x^3\right)^{\frac{m+1}{3}} \Gamma \left(\frac{m+1}{3},-2 i d x^3\right)+i b^2 m \sin (2 c) \left(i d x^3\right)^{\frac{m+1}{3}} \Gamma \left(\frac{m+1}{3},-2 i d x^3\right)+3 b^2 2^{\frac{m+4}{3}} \left(d^2 x^6\right)^{\frac{m+1}{3}}\right)}{3 (m+1)}","\frac{\left(2 a^2+b^2\right) (e x)^{m+1}}{2 e (m+1)}+\frac{i a b e^{i c} \left(-i d x^3\right)^{\frac{1}{3} (-m-1)} (e x)^{m+1} \Gamma \left(\frac{m+1}{3},-i d x^3\right)}{3 e}-\frac{i a b e^{-i c} \left(i d x^3\right)^{\frac{1}{3} (-m-1)} (e x)^{m+1} \Gamma \left(\frac{m+1}{3},i d x^3\right)}{3 e}+\frac{b^2 e^{2 i c} 2^{-\frac{m}{3}-\frac{7}{3}} \left(-i d x^3\right)^{\frac{1}{3} (-m-1)} (e x)^{m+1} \Gamma \left(\frac{m+1}{3},-2 i d x^3\right)}{3 e}+\frac{b^2 e^{-2 i c} 2^{-\frac{m}{3}-\frac{7}{3}} \left(i d x^3\right)^{\frac{1}{3} (-m-1)} (e x)^{m+1} \Gamma \left(\frac{m+1}{3},2 i d x^3\right)}{3 e}",1,"(2^((-7 - m)/3)*x*(e*x)^m*(d^2*x^6)^((-1 - m)/3)*(3*2^((7 + m)/3)*a^2*(d^2*x^6)^((1 + m)/3) + 3*2^((4 + m)/3)*b^2*(d^2*x^6)^((1 + m)/3) + b^2*(I*d*x^3)^((1 + m)/3)*Cos[2*c]*Gamma[(1 + m)/3, (-2*I)*d*x^3] + b^2*m*(I*d*x^3)^((1 + m)/3)*Cos[2*c]*Gamma[(1 + m)/3, (-2*I)*d*x^3] + b^2*((-I)*d*x^3)^((1 + m)/3)*Cos[2*c]*Gamma[(1 + m)/3, (2*I)*d*x^3] + b^2*m*((-I)*d*x^3)^((1 + m)/3)*Cos[2*c]*Gamma[(1 + m)/3, (2*I)*d*x^3] - I*2^((7 + m)/3)*a*b*(1 + m)*((-I)*d*x^3)^((1 + m)/3)*Gamma[(1 + m)/3, I*d*x^3]*(Cos[c] - I*Sin[c]) + I*2^((7 + m)/3)*a*b*(1 + m)*(I*d*x^3)^((1 + m)/3)*Gamma[(1 + m)/3, (-I)*d*x^3]*(Cos[c] + I*Sin[c]) + I*b^2*(I*d*x^3)^((1 + m)/3)*Gamma[(1 + m)/3, (-2*I)*d*x^3]*Sin[2*c] + I*b^2*m*(I*d*x^3)^((1 + m)/3)*Gamma[(1 + m)/3, (-2*I)*d*x^3]*Sin[2*c] - I*b^2*((-I)*d*x^3)^((1 + m)/3)*Gamma[(1 + m)/3, (2*I)*d*x^3]*Sin[2*c] - I*b^2*m*((-I)*d*x^3)^((1 + m)/3)*Gamma[(1 + m)/3, (2*I)*d*x^3]*Sin[2*c]))/(3*(1 + m))","A",1
100,1,149,134,1.5880522,"\int (e x)^m \left(a+b \sin \left(c+d x^3\right)\right) \, dx","Integrate[(e*x)^m*(a + b*Sin[c + d*x^3]),x]","\frac{x \left(d^2 x^6\right)^{\frac{1}{3} (-m-1)} (e x)^m \left(6 a \left(d^2 x^6\right)^{\frac{m+1}{3}}-i b (m+1) (\cos (c)-i \sin (c)) \left(-i d x^3\right)^{\frac{m+1}{3}} \Gamma \left(\frac{m+1}{3},i d x^3\right)+i b (m+1) (\cos (c)+i \sin (c)) \left(i d x^3\right)^{\frac{m+1}{3}} \Gamma \left(\frac{m+1}{3},-i d x^3\right)\right)}{6 (m+1)}","\frac{a (e x)^{m+1}}{e (m+1)}+\frac{i b e^{i c} \left(-i d x^3\right)^{\frac{1}{3} (-m-1)} (e x)^{m+1} \Gamma \left(\frac{m+1}{3},-i d x^3\right)}{6 e}-\frac{i b e^{-i c} \left(i d x^3\right)^{\frac{1}{3} (-m-1)} (e x)^{m+1} \Gamma \left(\frac{m+1}{3},i d x^3\right)}{6 e}",1,"(x*(e*x)^m*(d^2*x^6)^((-1 - m)/3)*(6*a*(d^2*x^6)^((1 + m)/3) - I*b*(1 + m)*((-I)*d*x^3)^((1 + m)/3)*Gamma[(1 + m)/3, I*d*x^3]*(Cos[c] - I*Sin[c]) + I*b*(1 + m)*(I*d*x^3)^((1 + m)/3)*Gamma[(1 + m)/3, (-I)*d*x^3]*(Cos[c] + I*Sin[c])))/(6*(1 + m))","A",1
101,0,0,23,0.4006857,"\int \frac{(e x)^m}{a+b \sin \left(c+d x^3\right)} \, dx","Integrate[(e*x)^m/(a + b*Sin[c + d*x^3]),x]","\int \frac{(e x)^m}{a+b \sin \left(c+d x^3\right)} \, dx","\text{Int}\left(\frac{(e x)^m}{a+b \sin \left(c+d x^3\right)},x\right)",0,"Integrate[(e*x)^m/(a + b*Sin[c + d*x^3]), x]","A",-1
102,0,0,23,1.0107805,"\int \frac{(e x)^m}{\left(a+b \sin \left(c+d x^3\right)\right)^2} \, dx","Integrate[(e*x)^m/(a + b*Sin[c + d*x^3])^2,x]","\int \frac{(e x)^m}{\left(a+b \sin \left(c+d x^3\right)\right)^2} \, dx","\text{Int}\left(\frac{(e x)^m}{\left(a+b \sin \left(c+d x^3\right)\right)^2},x\right)",0,"Integrate[(e*x)^m/(a + b*Sin[c + d*x^3])^2, x]","A",-1
103,1,70,78,0.0824118,"\int x^2 \sin \left(a+\frac{b}{x}\right) \, dx","Integrate[x^2*Sin[a + b/x],x]","\frac{1}{6} \left(b^3 \cos (a) \text{Ci}\left(\frac{b}{x}\right)-b^3 \sin (a) \text{Si}\left(\frac{b}{x}\right)+x \left(b^2 \left(-\sin \left(a+\frac{b}{x}\right)\right)+2 x^2 \sin \left(a+\frac{b}{x}\right)+b x \cos \left(a+\frac{b}{x}\right)\right)\right)","\frac{1}{6} b^3 \cos (a) \text{Ci}\left(\frac{b}{x}\right)-\frac{1}{6} b^3 \sin (a) \text{Si}\left(\frac{b}{x}\right)-\frac{1}{6} b^2 x \sin \left(a+\frac{b}{x}\right)+\frac{1}{3} x^3 \sin \left(a+\frac{b}{x}\right)+\frac{1}{6} b x^2 \cos \left(a+\frac{b}{x}\right)",1,"(b^3*Cos[a]*CosIntegral[b/x] + x*(b*x*Cos[a + b/x] - b^2*Sin[a + b/x] + 2*x^2*Sin[a + b/x]) - b^3*Sin[a]*SinIntegral[b/x])/6","A",1
104,1,52,60,0.0643387,"\int x \sin \left(a+\frac{b}{x}\right) \, dx","Integrate[x*Sin[a + b/x],x]","\frac{1}{2} \left(b^2 \sin (a) \text{Ci}\left(\frac{b}{x}\right)+b^2 \cos (a) \text{Si}\left(\frac{b}{x}\right)+x \left(x \sin \left(a+\frac{b}{x}\right)+b \cos \left(a+\frac{b}{x}\right)\right)\right)","\frac{1}{2} b^2 \sin (a) \text{Ci}\left(\frac{b}{x}\right)+\frac{1}{2} b^2 \cos (a) \text{Si}\left(\frac{b}{x}\right)+\frac{1}{2} x^2 \sin \left(a+\frac{b}{x}\right)+\frac{1}{2} b x \cos \left(a+\frac{b}{x}\right)",1,"(b^2*CosIntegral[b/x]*Sin[a] + x*(b*Cos[a + b/x] + x*Sin[a + b/x]) + b^2*Cos[a]*SinIntegral[b/x])/2","A",1
105,1,32,32,0.0254269,"\int \sin \left(a+\frac{b}{x}\right) \, dx","Integrate[Sin[a + b/x],x]","-b \cos (a) \text{Ci}\left(\frac{b}{x}\right)+b \sin (a) \text{Si}\left(\frac{b}{x}\right)+x \sin \left(a+\frac{b}{x}\right)","-b \cos (a) \text{Ci}\left(\frac{b}{x}\right)+b \sin (a) \text{Si}\left(\frac{b}{x}\right)+x \sin \left(a+\frac{b}{x}\right)",1,"-(b*Cos[a]*CosIntegral[b/x]) + x*Sin[a + b/x] + b*Sin[a]*SinIntegral[b/x]","A",1
106,1,21,21,0.0515445,"\int \frac{\sin \left(a+\frac{b}{x}\right)}{x} \, dx","Integrate[Sin[a + b/x]/x,x]","\sin (a) \left(-\text{Ci}\left(\frac{b}{x}\right)\right)-\cos (a) \text{Si}\left(\frac{b}{x}\right)","\sin (a) \left(-\text{Ci}\left(\frac{b}{x}\right)\right)-\cos (a) \text{Si}\left(\frac{b}{x}\right)",1,"-(CosIntegral[b/x]*Sin[a]) - Cos[a]*SinIntegral[b/x]","A",1
107,1,12,12,0.0140883,"\int \frac{\sin \left(a+\frac{b}{x}\right)}{x^2} \, dx","Integrate[Sin[a + b/x]/x^2,x]","\frac{\cos \left(a+\frac{b}{x}\right)}{b}","\frac{\cos \left(a+\frac{b}{x}\right)}{b}",1,"Cos[a + b/x]/b","A",1
108,1,29,29,0.0035467,"\int \frac{\sin \left(a+\frac{b}{x}\right)}{x^3} \, dx","Integrate[Sin[a + b/x]/x^3,x]","\frac{\cos \left(a+\frac{b}{x}\right)}{b x}-\frac{\sin \left(a+\frac{b}{x}\right)}{b^2}","\frac{\cos \left(a+\frac{b}{x}\right)}{b x}-\frac{\sin \left(a+\frac{b}{x}\right)}{b^2}",1,"Cos[a + b/x]/(b*x) - Sin[a + b/x]/b^2","A",1
109,1,38,45,0.0594058,"\int \frac{\sin \left(a+\frac{b}{x}\right)}{x^4} \, dx","Integrate[Sin[a + b/x]/x^4,x]","\frac{\left(b^2-2 x^2\right) \cos \left(a+\frac{b}{x}\right)-2 b x \sin \left(a+\frac{b}{x}\right)}{b^3 x^2}","-\frac{2 \cos \left(a+\frac{b}{x}\right)}{b^3}-\frac{2 \sin \left(a+\frac{b}{x}\right)}{b^2 x}+\frac{\cos \left(a+\frac{b}{x}\right)}{b x^2}",1,"((b^2 - 2*x^2)*Cos[a + b/x] - 2*b*x*Sin[a + b/x])/(b^3*x^2)","A",1
110,1,61,61,0.0046425,"\int \frac{\sin \left(a+\frac{b}{x}\right)}{x^5} \, dx","Integrate[Sin[a + b/x]/x^5,x]","\frac{6 \sin \left(a+\frac{b}{x}\right)}{b^4}-\frac{6 \cos \left(a+\frac{b}{x}\right)}{b^3 x}-\frac{3 \sin \left(a+\frac{b}{x}\right)}{b^2 x^2}+\frac{\cos \left(a+\frac{b}{x}\right)}{b x^3}","\frac{6 \sin \left(a+\frac{b}{x}\right)}{b^4}-\frac{6 \cos \left(a+\frac{b}{x}\right)}{b^3 x}-\frac{3 \sin \left(a+\frac{b}{x}\right)}{b^2 x^2}+\frac{\cos \left(a+\frac{b}{x}\right)}{b x^3}",1,"Cos[a + b/x]/(b*x^3) - (6*Cos[a + b/x])/(b^3*x) + (6*Sin[a + b/x])/b^4 - (3*Sin[a + b/x])/(b^2*x^2)","A",1
111,1,86,97,0.1765021,"\int x^2 \sin ^2\left(a+\frac{b}{x}\right) \, dx","Integrate[x^2*Sin[a + b/x]^2,x]","\frac{1}{6} \left(4 b^3 \sin (2 a) \text{Ci}\left(\frac{2 b}{x}\right)+4 b^3 \cos (2 a) \text{Si}\left(\frac{2 b}{x}\right)+x \left(2 b^2 \cos \left(2 \left(a+\frac{b}{x}\right)\right)-x^2 \cos \left(2 \left(a+\frac{b}{x}\right)\right)+b x \sin \left(2 \left(a+\frac{b}{x}\right)\right)+x^2\right)\right)","\frac{2}{3} b^3 \sin (2 a) \text{Ci}\left(\frac{2 b}{x}\right)+\frac{2}{3} b^3 \cos (2 a) \text{Si}\left(\frac{2 b}{x}\right)+\frac{1}{3} b^2 x \cos \left(2 \left(a+\frac{b}{x}\right)\right)-\frac{1}{6} x^3 \cos \left(2 \left(a+\frac{b}{x}\right)\right)+\frac{1}{6} b x^2 \sin \left(2 \left(a+\frac{b}{x}\right)\right)+\frac{x^3}{6}",1,"(4*b^3*CosIntegral[(2*b)/x]*Sin[2*a] + x*(x^2 + 2*b^2*Cos[2*(a + b/x)] - x^2*Cos[2*(a + b/x)] + b*x*Sin[2*(a + b/x)]) + 4*b^3*Cos[2*a]*SinIntegral[(2*b)/x])/6","A",1
112,1,65,65,0.1661049,"\int x \sin ^2\left(a+\frac{b}{x}\right) \, dx","Integrate[x*Sin[a + b/x]^2,x]","b^2 (-\cos (2 a)) \text{Ci}\left(\frac{2 b}{x}\right)+b^2 \sin (2 a) \text{Si}\left(\frac{2 b}{x}\right)+\frac{1}{4} x \left(2 b \sin \left(2 \left(a+\frac{b}{x}\right)\right)+x \left(-\cos \left(2 \left(a+\frac{b}{x}\right)\right)\right)+x\right)","b^2 (-\cos (2 a)) \text{Ci}\left(\frac{2 b}{x}\right)+b^2 \sin (2 a) \text{Si}\left(\frac{2 b}{x}\right)+\frac{1}{2} x^2 \sin ^2\left(a+\frac{b}{x}\right)+\frac{1}{2} b x \sin \left(2 \left(a+\frac{b}{x}\right)\right)",1,"-(b^2*Cos[2*a]*CosIntegral[(2*b)/x]) + (x*(x - x*Cos[2*(a + b/x)] + 2*b*Sin[2*(a + b/x)]))/4 + b^2*Sin[2*a]*SinIntegral[(2*b)/x]","A",1
113,1,41,41,0.08902,"\int \sin ^2\left(a+\frac{b}{x}\right) \, dx","Integrate[Sin[a + b/x]^2,x]","-b \sin (2 a) \text{Ci}\left(\frac{2 b}{x}\right)-b \cos (2 a) \text{Si}\left(\frac{2 b}{x}\right)+x \sin ^2\left(a+\frac{b}{x}\right)","-b \sin (2 a) \text{Ci}\left(\frac{2 b}{x}\right)-b \cos (2 a) \text{Si}\left(\frac{2 b}{x}\right)+x \sin ^2\left(a+\frac{b}{x}\right)",1,"-(b*CosIntegral[(2*b)/x]*Sin[2*a]) + x*Sin[a + b/x]^2 - b*Cos[2*a]*SinIntegral[(2*b)/x]","A",1
114,1,32,37,0.0555503,"\int \frac{\sin ^2\left(a+\frac{b}{x}\right)}{x} \, dx","Integrate[Sin[a + b/x]^2/x,x]","\frac{1}{2} \left(\cos (2 a) \text{Ci}\left(\frac{2 b}{x}\right)-\sin (2 a) \text{Si}\left(\frac{2 b}{x}\right)+\log (x)\right)","\frac{1}{2} \cos (2 a) \text{Ci}\left(\frac{2 b}{x}\right)-\frac{1}{2} \sin (2 a) \text{Si}\left(\frac{2 b}{x}\right)+\frac{\log (x)}{2}",1,"(Cos[2*a]*CosIntegral[(2*b)/x] + Log[x] - Sin[2*a]*SinIntegral[(2*b)/x])/2","A",1
115,1,32,31,0.0557049,"\int \frac{\sin ^2\left(a+\frac{b}{x}\right)}{x^2} \, dx","Integrate[Sin[a + b/x]^2/x^2,x]","\frac{\sin \left(2 \left(a+\frac{b}{x}\right)\right)}{4 b}-\frac{a+\frac{b}{x}}{2 b}","\frac{\sin \left(a+\frac{b}{x}\right) \cos \left(a+\frac{b}{x}\right)}{2 b}-\frac{1}{2 x}",1,"-1/2*(a + b/x)/b + Sin[2*(a + b/x)]/(4*b)","A",1
116,1,43,51,0.085674,"\int \frac{\sin ^2\left(a+\frac{b}{x}\right)}{x^3} \, dx","Integrate[Sin[a + b/x]^2/x^3,x]","\frac{x^2 \cos \left(2 \left(a+\frac{b}{x}\right)\right)-2 b \left(b-x \sin \left(2 \left(a+\frac{b}{x}\right)\right)\right)}{8 b^2 x^2}","-\frac{\sin ^2\left(a+\frac{b}{x}\right)}{4 b^2}+\frac{\sin \left(a+\frac{b}{x}\right) \cos \left(a+\frac{b}{x}\right)}{2 b x}-\frac{1}{4 x^2}",1,"(x^2*Cos[2*(a + b/x)] - 2*b*(b - x*Sin[2*(a + b/x)]))/(8*b^2*x^2)","A",1
117,1,54,87,0.1340075,"\int \frac{\sin ^2\left(a+\frac{b}{x}\right)}{x^4} \, dx","Integrate[Sin[a + b/x]^2/x^4,x]","\frac{-3 \left(x^3-2 b^2 x\right) \sin \left(2 \left(a+\frac{b}{x}\right)\right)+6 b x^2 \cos \left(2 \left(a+\frac{b}{x}\right)\right)-4 b^3}{24 b^3 x^3}","-\frac{\sin \left(a+\frac{b}{x}\right) \cos \left(a+\frac{b}{x}\right)}{4 b^3}-\frac{\sin ^2\left(a+\frac{b}{x}\right)}{2 b^2 x}+\frac{\sin \left(a+\frac{b}{x}\right) \cos \left(a+\frac{b}{x}\right)}{2 b x^2}+\frac{1}{4 b^2 x}-\frac{1}{6 x^3}",1,"(-4*b^3 + 6*b*x^2*Cos[2*(a + b/x)] - 3*(-2*b^2*x + x^3)*Sin[2*(a + b/x)])/(24*b^3*x^3)","A",1
118,1,65,107,0.1963098,"\int \frac{\sin ^2\left(a+\frac{b}{x}\right)}{x^5} \, dx","Integrate[Sin[a + b/x]^2/x^5,x]","-\frac{3 \left(x^4-2 b^2 x^2\right) \cos \left(2 \left(a+\frac{b}{x}\right)\right)+2 b \left(\left(3 x^3-2 b^2 x\right) \sin \left(2 \left(a+\frac{b}{x}\right)\right)+b^3\right)}{16 b^4 x^4}","\frac{3 \sin ^2\left(a+\frac{b}{x}\right)}{8 b^4}-\frac{3 \sin \left(a+\frac{b}{x}\right) \cos \left(a+\frac{b}{x}\right)}{4 b^3 x}-\frac{3 \sin ^2\left(a+\frac{b}{x}\right)}{4 b^2 x^2}+\frac{\sin \left(a+\frac{b}{x}\right) \cos \left(a+\frac{b}{x}\right)}{2 b x^3}+\frac{3}{8 b^2 x^2}-\frac{1}{8 x^4}",1,"-1/16*(3*(-2*b^2*x^2 + x^4)*Cos[2*(a + b/x)] + 2*b*(b^3 + (-2*b^2*x + 3*x^3)*Sin[2*(a + b/x)]))/(b^4*x^4)","A",1
119,1,81,80,0.1361058,"\int \sin \left(a+\frac{b}{x^2}\right) \, dx","Integrate[Sin[a + b/x^2],x]","-\sqrt{2 \pi } \sqrt{b} \left(\cos (a) C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{x}\right)-\sin (a) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{x}\right)\right)+x \sin (a) \cos \left(\frac{b}{x^2}\right)+x \cos (a) \sin \left(\frac{b}{x^2}\right)","\sqrt{2 \pi } \left(-\sqrt{b}\right) \cos (a) C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{x}\right)+\sqrt{2 \pi } \sqrt{b} \sin (a) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{x}\right)+x \sin \left(a+\frac{b}{x^2}\right)",1,"x*Cos[b/x^2]*Sin[a] - Sqrt[b]*Sqrt[2*Pi]*(Cos[a]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/x] - FresnelS[(Sqrt[b]*Sqrt[2/Pi])/x]*Sin[a]) + x*Cos[a]*Sin[b/x^2]","A",1
120,1,25,25,0.0482816,"\int \frac{\sin \left(a+\frac{b}{x^2}\right)}{x} \, dx","Integrate[Sin[a + b/x^2]/x,x]","\frac{1}{2} \left(\sin (a) \left(-\text{Ci}\left(\frac{b}{x^2}\right)\right)-\cos (a) \text{Si}\left(\frac{b}{x^2}\right)\right)","-\frac{1}{2} \sin (a) \text{Ci}\left(\frac{b}{x^2}\right)-\frac{1}{2} \cos (a) \text{Si}\left(\frac{b}{x^2}\right)",1,"(-(CosIntegral[b/x^2]*Sin[a]) - Cos[a]*SinIntegral[b/x^2])/2","A",1
121,1,61,75,0.1018903,"\int \frac{\sin \left(a+\frac{b}{x^2}\right)}{x^2} \, dx","Integrate[Sin[a + b/x^2]/x^2,x]","-\frac{\sqrt{\frac{\pi }{2}} \left(\sin (a) C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{x}\right)+\cos (a) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{x}\right)\right)}{\sqrt{b}}","-\frac{\sqrt{\frac{\pi }{2}} \sin (a) C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{x}\right)}{\sqrt{b}}-\frac{\sqrt{\frac{\pi }{2}} \cos (a) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{x}\right)}{\sqrt{b}}",1,"-((Sqrt[Pi/2]*(Cos[a]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/x] + FresnelC[(Sqrt[b]*Sqrt[2/Pi])/x]*Sin[a]))/Sqrt[b])","A",1
122,1,15,15,0.0140116,"\int \frac{\sin \left(a+\frac{b}{x^2}\right)}{x^3} \, dx","Integrate[Sin[a + b/x^2]/x^3,x]","\frac{\cos \left(a+\frac{b}{x^2}\right)}{2 b}","\frac{\cos \left(a+\frac{b}{x^2}\right)}{2 b}",1,"Cos[a + b/x^2]/(2*b)","A",1
123,1,89,97,0.1601263,"\int \frac{\sin \left(a+\frac{b}{x^2}\right)}{x^4} \, dx","Integrate[Sin[a + b/x^2]/x^4,x]","\frac{-\sqrt{2 \pi } x \cos (a) C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{x}\right)+\sqrt{2 \pi } x \sin (a) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{x}\right)+2 \sqrt{b} \cos \left(a+\frac{b}{x^2}\right)}{4 b^{3/2} x}","-\frac{\sqrt{\frac{\pi }{2}} \cos (a) C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{x}\right)}{2 b^{3/2}}+\frac{\sqrt{\frac{\pi }{2}} \sin (a) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{x}\right)}{2 b^{3/2}}+\frac{\cos \left(a+\frac{b}{x^2}\right)}{2 b x}",1,"(2*Sqrt[b]*Cos[a + b/x^2] - Sqrt[2*Pi]*x*Cos[a]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/x] + Sqrt[2*Pi]*x*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/x]*Sin[a])/(4*b^(3/2)*x)","A",1
124,1,8,8,0.0110078,"\int \frac{\sin \left(\sqrt{x}\right)}{\sqrt{x}} \, dx","Integrate[Sin[Sqrt[x]]/Sqrt[x],x]","-2 \cos \left(\sqrt{x}\right)","-2 \cos \left(\sqrt{x}\right)",1,"-2*Cos[Sqrt[x]]","A",1
125,1,23,21,0.0241822,"\int \frac{\sin ^3\left(\sqrt{x}\right)}{\sqrt{x}} \, dx","Integrate[Sin[Sqrt[x]]^3/Sqrt[x],x]","\frac{1}{6} \cos \left(3 \sqrt{x}\right)-\frac{3 \cos \left(\sqrt{x}\right)}{2}","\frac{2}{3} \cos ^3\left(\sqrt{x}\right)-2 \cos \left(\sqrt{x}\right)",1,"(-3*Cos[Sqrt[x]])/2 + Cos[3*Sqrt[x]]/6","A",1
126,1,22,22,0.0191689,"\int \sin \left(\sqrt{x}\right) \, dx","Integrate[Sin[Sqrt[x]],x]","2 \sin \left(\sqrt{x}\right)-2 \sqrt{x} \cos \left(\sqrt{x}\right)","2 \sin \left(\sqrt{x}\right)-2 \sqrt{x} \cos \left(\sqrt{x}\right)",1,"-2*Sqrt[x]*Cos[Sqrt[x]] + 2*Sin[Sqrt[x]]","A",1
127,1,41,69,0.0483198,"\int \sin ^2\left(\sqrt[3]{x}\right) \, dx","Integrate[Sin[x^(1/3)]^2,x]","\frac{1}{8} \left(\left(3-6 x^{2/3}\right) \sin \left(2 \sqrt[3]{x}\right)+4 x-6 \sqrt[3]{x} \cos \left(2 \sqrt[3]{x}\right)\right)","-\frac{3}{2} x^{2/3} \sin \left(\sqrt[3]{x}\right) \cos \left(\sqrt[3]{x}\right)+\frac{x}{2}-\frac{3 \sqrt[3]{x}}{4}+\frac{3}{2} \sqrt[3]{x} \sin ^2\left(\sqrt[3]{x}\right)+\frac{3}{4} \sin \left(\sqrt[3]{x}\right) \cos \left(\sqrt[3]{x}\right)",1,"(4*x - 6*x^(1/3)*Cos[2*x^(1/3)] + (3 - 6*x^(2/3))*Sin[2*x^(1/3)])/8","A",1
128,1,62,87,0.0555399,"\int \sin ^3\left(\sqrt[3]{x}\right) \, dx","Integrate[Sin[x^(1/3)]^3,x]","\frac{1}{36} \left(-81 \left(x^{2/3}-2\right) \cos \left(\sqrt[3]{x}\right)+\left(9 x^{2/3}-2\right) \cos \left(3 \sqrt[3]{x}\right)-6 \sqrt[3]{x} \left(\sin \left(3 \sqrt[3]{x}\right)-27 \sin \left(\sqrt[3]{x}\right)\right)\right)","-2 x^{2/3} \cos \left(\sqrt[3]{x}\right)-x^{2/3} \sin ^2\left(\sqrt[3]{x}\right) \cos \left(\sqrt[3]{x}\right)+\frac{2}{3} \sqrt[3]{x} \sin ^3\left(\sqrt[3]{x}\right)+4 \sqrt[3]{x} \sin \left(\sqrt[3]{x}\right)-\frac{2}{9} \cos ^3\left(\sqrt[3]{x}\right)+\frac{14}{3} \cos \left(\sqrt[3]{x}\right)",1,"(-81*(-2 + x^(2/3))*Cos[x^(1/3)] + (-2 + 9*x^(2/3))*Cos[3*x^(1/3)] - 6*x^(1/3)*(-27*Sin[x^(1/3)] + Sin[3*x^(1/3)]))/36","A",1
129,0,0,21,1.0492289,"\int (e x)^m \left(b \sin \left(c+d x^n\right)\right)^p \, dx","Integrate[(e*x)^m*(b*Sin[c + d*x^n])^p,x]","\int (e x)^m \left(b \sin \left(c+d x^n\right)\right)^p \, dx","\text{Int}\left((e x)^m \left(b \sin \left(c+d x^n\right)\right)^p,x\right)",0,"Integrate[(e*x)^m*(b*Sin[c + d*x^n])^p, x]","A",-1
130,0,0,23,1.4557963,"\int (e x)^m \left(a+b \sin \left(c+d x^n\right)\right)^p \, dx","Integrate[(e*x)^m*(a + b*Sin[c + d*x^n])^p,x]","\int (e x)^m \left(a+b \sin \left(c+d x^n\right)\right)^p \, dx","\text{Int}\left((e x)^m \left(a+b \sin \left(c+d x^n\right)\right)^p,x\right)",0,"Integrate[(e*x)^m*(a + b*Sin[c + d*x^n])^p, x]","A",-1
131,1,88,92,0.1590448,"\int (e x)^{-1+n} \left(b \sin \left(c+d x^n\right)\right)^p \, dx","Integrate[(e*x)^(-1 + n)*(b*Sin[c + d*x^n])^p,x]","\frac{x^{1-n} (e x)^{n-1} \sqrt{\cos ^2\left(c+d x^n\right)} \tan \left(c+d x^n\right) \left(b \sin \left(c+d x^n\right)\right)^p \, _2F_1\left(\frac{1}{2},\frac{p+1}{2};\frac{p+3}{2};\sin ^2\left(d x^n+c\right)\right)}{d n (p+1)}","\frac{x^{-n} (e x)^n \cos \left(c+d x^n\right) \left(b \sin \left(c+d x^n\right)\right)^{p+1} \, _2F_1\left(\frac{1}{2},\frac{p+1}{2};\frac{p+3}{2};\sin ^2\left(d x^n+c\right)\right)}{b d e n (p+1) \sqrt{\cos ^2\left(c+d x^n\right)}}",1,"(x^(1 - n)*(e*x)^(-1 + n)*Sqrt[Cos[c + d*x^n]^2]*Hypergeometric2F1[1/2, (1 + p)/2, (3 + p)/2, Sin[c + d*x^n]^2]*(b*Sin[c + d*x^n])^p*Tan[c + d*x^n])/(d*n*(1 + p))","A",1
132,0,0,39,0.9349177,"\int (e x)^{-1+2 n} \left(b \sin \left(c+d x^n\right)\right)^p \, dx","Integrate[(e*x)^(-1 + 2*n)*(b*Sin[c + d*x^n])^p,x]","\int (e x)^{-1+2 n} \left(b \sin \left(c+d x^n\right)\right)^p \, dx","\frac{x^{-2 n} (e x)^{2 n} \text{Int}\left(x^{2 n-1} \left(b \sin \left(c+d x^n\right)\right)^p,x\right)}{e}",0,"Integrate[(e*x)^(-1 + 2*n)*(b*Sin[c + d*x^n])^p, x]","A",-1
133,1,148,132,0.4638238,"\int (e x)^{-1+n} \left(a+b \sin \left(c+d x^n\right)\right)^p \, dx","Integrate[(e*x)^(-1 + n)*(a + b*Sin[c + d*x^n])^p,x]","\frac{x^{-n} (e x)^n \sec \left(c+d x^n\right) \sqrt{-\frac{b \left(\sin \left(c+d x^n\right)-1\right)}{a+b}} \sqrt{\frac{b \left(\sin \left(c+d x^n\right)+1\right)}{b-a}} \left(a+b \sin \left(c+d x^n\right)\right)^{p+1} F_1\left(p+1;\frac{1}{2},\frac{1}{2};p+2;\frac{a+b \sin \left(d x^n+c\right)}{a-b},\frac{a+b \sin \left(d x^n+c\right)}{a+b}\right)}{b d e n (p+1)}","-\frac{\sqrt{2} x^{-n} (e x)^n \cos \left(c+d x^n\right) \left(a+b \sin \left(c+d x^n\right)\right)^p \left(\frac{a+b \sin \left(c+d x^n\right)}{a+b}\right)^{-p} F_1\left(\frac{1}{2};\frac{1}{2},-p;\frac{3}{2};\frac{1}{2} \left(1-\sin \left(d x^n+c\right)\right),\frac{b \left(1-\sin \left(d x^n+c\right)\right)}{a+b}\right)}{d e n \sqrt{\sin \left(c+d x^n\right)+1}}",1,"((e*x)^n*AppellF1[1 + p, 1/2, 1/2, 2 + p, (a + b*Sin[c + d*x^n])/(a - b), (a + b*Sin[c + d*x^n])/(a + b)]*Sec[c + d*x^n]*Sqrt[-((b*(-1 + Sin[c + d*x^n]))/(a + b))]*Sqrt[(b*(1 + Sin[c + d*x^n]))/(-a + b)]*(a + b*Sin[c + d*x^n])^(1 + p))/(b*d*e*n*(1 + p)*x^n)","A",0
134,0,0,41,1.2975425,"\int (e x)^{-1+2 n} \left(a+b \sin \left(c+d x^n\right)\right)^p \, dx","Integrate[(e*x)^(-1 + 2*n)*(a + b*Sin[c + d*x^n])^p,x]","\int (e x)^{-1+2 n} \left(a+b \sin \left(c+d x^n\right)\right)^p \, dx","\frac{x^{-2 n} (e x)^{2 n} \text{Int}\left(x^{2 n-1} \left(a+b \sin \left(c+d x^n\right)\right)^p,x\right)}{e}",0,"Integrate[(e*x)^(-1 + 2*n)*(a + b*Sin[c + d*x^n])^p, x]","A",-1
135,1,23,25,0.0669874,"\int \frac{\sin \left(a+b x^n\right)}{x} \, dx","Integrate[Sin[a + b*x^n]/x,x]","\frac{\sin (a) \text{Ci}\left(b x^n\right)+\cos (a) \text{Si}\left(b x^n\right)}{n}","\frac{\sin (a) \text{Ci}\left(b x^n\right)}{n}+\frac{\cos (a) \text{Si}\left(b x^n\right)}{n}",1,"(CosIntegral[b*x^n]*Sin[a] + Cos[a]*SinIntegral[b*x^n])/n","A",1
136,1,37,43,0.0805902,"\int \frac{\sin ^2\left(a+b x^n\right)}{x} \, dx","Integrate[Sin[a + b*x^n]^2/x,x]","\frac{-\cos (2 a) \text{Ci}\left(2 b x^n\right)+\sin (2 a) \text{Si}\left(2 b x^n\right)+n \log (x)}{2 n}","-\frac{\cos (2 a) \text{Ci}\left(2 b x^n\right)}{2 n}+\frac{\sin (2 a) \text{Si}\left(2 b x^n\right)}{2 n}+\frac{\log (x)}{2}",1,"(-(Cos[2*a]*CosIntegral[2*b*x^n]) + n*Log[x] + Sin[2*a]*SinIntegral[2*b*x^n])/(2*n)","A",1
137,1,54,67,0.1119532,"\int \frac{\sin ^3\left(a+b x^n\right)}{x} \, dx","Integrate[Sin[a + b*x^n]^3/x,x]","\frac{3 \sin (a) \text{Ci}\left(b x^n\right)-\sin (3 a) \text{Ci}\left(3 b x^n\right)+3 \cos (a) \text{Si}\left(b x^n\right)-\cos (3 a) \text{Si}\left(3 b x^n\right)}{4 n}","\frac{3 \sin (a) \text{Ci}\left(b x^n\right)}{4 n}-\frac{\sin (3 a) \text{Ci}\left(3 b x^n\right)}{4 n}+\frac{3 \cos (a) \text{Si}\left(b x^n\right)}{4 n}-\frac{\cos (3 a) \text{Si}\left(3 b x^n\right)}{4 n}",1,"(3*CosIntegral[b*x^n]*Sin[a] - CosIntegral[3*b*x^n]*Sin[3*a] + 3*Cos[a]*SinIntegral[b*x^n] - Cos[3*a]*SinIntegral[3*b*x^n])/(4*n)","A",1
138,1,66,79,0.1155109,"\int \frac{\sin ^4\left(a+b x^n\right)}{x} \, dx","Integrate[Sin[a + b*x^n]^4/x,x]","\frac{-4 \cos (2 a) \text{Ci}\left(2 b x^n\right)+\cos (4 a) \text{Ci}\left(4 b x^n\right)+4 \sin (2 a) \text{Si}\left(2 b x^n\right)-\sin (4 a) \text{Si}\left(4 b x^n\right)}{8 n}+\frac{3 \log (x)}{8}","-\frac{\cos (2 a) \text{Ci}\left(2 b x^n\right)}{2 n}+\frac{\cos (4 a) \text{Ci}\left(4 b x^n\right)}{8 n}+\frac{\sin (2 a) \text{Si}\left(2 b x^n\right)}{2 n}-\frac{\sin (4 a) \text{Si}\left(4 b x^n\right)}{8 n}+\frac{3 \log (x)}{8}",1,"(3*Log[x])/8 + (-4*Cos[2*a]*CosIntegral[2*b*x^n] + Cos[4*a]*CosIntegral[4*b*x^n] + 4*Sin[2*a]*SinIntegral[2*b*x^n] - Sin[4*a]*SinIntegral[4*b*x^n])/(8*n)","A",1
139,1,95,87,0.0887731,"\int \sin \left(a+b x^n\right) \, dx","Integrate[Sin[a + b*x^n],x]","\frac{i x \left(b^2 x^{2 n}\right)^{-1/n} \left((\cos (a)+i \sin (a)) \left(i b x^n\right)^{\frac{1}{n}} \Gamma \left(\frac{1}{n},-i b x^n\right)-(\cos (a)-i \sin (a)) \left(-i b x^n\right)^{\frac{1}{n}} \Gamma \left(\frac{1}{n},i b x^n\right)\right)}{2 n}","\frac{i e^{i a} x \left(-i b x^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-i b x^n\right)}{2 n}-\frac{i e^{-i a} x \left(i b x^n\right)^{-1/n} \Gamma \left(\frac{1}{n},i b x^n\right)}{2 n}",1,"((I/2)*x*(-(((-I)*b*x^n)^n^(-1)*Gamma[n^(-1), I*b*x^n]*(Cos[a] - I*Sin[a])) + (I*b*x^n)^n^(-1)*Gamma[n^(-1), (-I)*b*x^n]*(Cos[a] + I*Sin[a])))/(n*(b^2*x^(2*n))^n^(-1))","A",1
140,1,94,100,0.2339751,"\int \sin ^2\left(a+b x^n\right) \, dx","Integrate[Sin[a + b*x^n]^2,x]","\frac{x \left(e^{2 i a} 2^{-1/n} \left(-i b x^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-2 i b x^n\right)+e^{-2 i a} 2^{-1/n} \left(i b x^n\right)^{-1/n} \Gamma \left(\frac{1}{n},2 i b x^n\right)+2 n\right)}{4 n}","\frac{e^{2 i a} 2^{-\frac{1}{n}-2} x \left(-i b x^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-2 i b x^n\right)}{n}+\frac{e^{-2 i a} 2^{-\frac{1}{n}-2} x \left(i b x^n\right)^{-1/n} \Gamma \left(\frac{1}{n},2 i b x^n\right)}{n}+\frac{x}{2}",1,"(x*(2*n + (E^((2*I)*a)*Gamma[n^(-1), (-2*I)*b*x^n])/(2^n^(-1)*((-I)*b*x^n)^n^(-1)) + Gamma[n^(-1), (2*I)*b*x^n]/(2^n^(-1)*E^((2*I)*a)*(I*b*x^n)^n^(-1))))/(4*n)","A",1
141,1,177,187,0.2939403,"\int \sin ^3\left(a+b x^n\right) \, dx","Integrate[Sin[a + b*x^n]^3,x]","\frac{i e^{-3 i a} 3^{-1/n} x \left(b^2 x^{2 n}\right)^{-1/n} \left(e^{2 i a} \left(-3^{\frac{1}{n}+1}\right) \left(-i b x^n\right)^{\frac{1}{n}} \Gamma \left(\frac{1}{n},i b x^n\right)+e^{4 i a} 3^{\frac{1}{n}+1} \left(i b x^n\right)^{\frac{1}{n}} \Gamma \left(\frac{1}{n},-i b x^n\right)-e^{6 i a} \left(i b x^n\right)^{\frac{1}{n}} \Gamma \left(\frac{1}{n},-3 i b x^n\right)+\left(-i b x^n\right)^{\frac{1}{n}} \Gamma \left(\frac{1}{n},3 i b x^n\right)\right)}{8 n}","\frac{3 i e^{i a} x \left(-i b x^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-i b x^n\right)}{8 n}-\frac{i e^{3 i a} 3^{-1/n} x \left(-i b x^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-3 i b x^n\right)}{8 n}-\frac{3 i e^{-i a} x \left(i b x^n\right)^{-1/n} \Gamma \left(\frac{1}{n},i b x^n\right)}{8 n}+\frac{i e^{-3 i a} 3^{-1/n} x \left(i b x^n\right)^{-1/n} \Gamma \left(\frac{1}{n},3 i b x^n\right)}{8 n}",1,"((I/8)*x*(3^(1 + n^(-1))*E^((4*I)*a)*(I*b*x^n)^n^(-1)*Gamma[n^(-1), (-I)*b*x^n] - 3^(1 + n^(-1))*E^((2*I)*a)*((-I)*b*x^n)^n^(-1)*Gamma[n^(-1), I*b*x^n] - E^((6*I)*a)*(I*b*x^n)^n^(-1)*Gamma[n^(-1), (-3*I)*b*x^n] + ((-I)*b*x^n)^n^(-1)*Gamma[n^(-1), (3*I)*b*x^n]))/(3^n^(-1)*E^((3*I)*a)*n*(b^2*x^(2*n))^n^(-1))","A",1
142,1,118,109,0.224815,"\int x^m \sin \left(a+b x^n\right) \, dx","Integrate[x^m*Sin[a + b*x^n],x]","\frac{i x^{m+1} \left(b^2 x^{2 n}\right)^{-\frac{m+1}{n}} \left((\cos (a)+i \sin (a)) \left(i b x^n\right)^{\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-i b x^n\right)-(\cos (a)-i \sin (a)) \left(-i b x^n\right)^{\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},i b x^n\right)\right)}{2 n}","\frac{i e^{i a} x^{m+1} \left(-i b x^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-i b x^n\right)}{2 n}-\frac{i e^{-i a} x^{m+1} \left(i b x^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},i b x^n\right)}{2 n}",1,"((I/2)*x^(1 + m)*(-(((-I)*b*x^n)^((1 + m)/n)*Gamma[(1 + m)/n, I*b*x^n]*(Cos[a] - I*Sin[a])) + (I*b*x^n)^((1 + m)/n)*Gamma[(1 + m)/n, (-I)*b*x^n]*(Cos[a] + I*Sin[a])))/(n*(b^2*x^(2*n))^((1 + m)/n))","A",1
143,1,129,139,0.537532,"\int x^m \sin ^2\left(a+b x^n\right) \, dx","Integrate[x^m*Sin[a + b*x^n]^2,x]","\frac{x^{m+1} \left(e^{2 i a} (m+1) 2^{-\frac{m+1}{n}} \left(-i b x^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-2 i b x^n\right)+e^{-2 i a} (m+1) 2^{-\frac{m+1}{n}} \left(i b x^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},2 i b x^n\right)+2 n\right)}{4 (m+1) n}","\frac{e^{2 i a} 2^{-\frac{m+2 n+1}{n}} x^{m+1} \left(-i b x^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-2 i b x^n\right)}{n}+\frac{e^{-2 i a} 2^{-\frac{m+2 n+1}{n}} x^{m+1} \left(i b x^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},2 i b x^n\right)}{n}+\frac{x^{m+1}}{2 (m+1)}",1,"(x^(1 + m)*(2*n + (E^((2*I)*a)*(1 + m)*Gamma[(1 + m)/n, (-2*I)*b*x^n])/(2^((1 + m)/n)*((-I)*b*x^n)^((1 + m)/n)) + ((1 + m)*Gamma[(1 + m)/n, (2*I)*b*x^n])/(2^((1 + m)/n)*E^((2*I)*a)*(I*b*x^n)^((1 + m)/n))))/(4*(1 + m)*n)","A",1
144,1,225,237,0.5991665,"\int x^m \sin ^3\left(a+b x^n\right) \, dx","Integrate[x^m*Sin[a + b*x^n]^3,x]","\frac{i e^{-3 i a} 3^{-\frac{m+1}{n}} x^{m+1} \left(b^2 x^{2 n}\right)^{-\frac{m+1}{n}} \left(e^{2 i a} \left(-3^{\frac{m+n+1}{n}}\right) \left(-i b x^n\right)^{\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},i b x^n\right)+e^{4 i a} 3^{\frac{m+n+1}{n}} \left(i b x^n\right)^{\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-i b x^n\right)-e^{6 i a} \left(i b x^n\right)^{\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-3 i b x^n\right)+\left(-i b x^n\right)^{\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},3 i b x^n\right)\right)}{8 n}","\frac{3 i e^{i a} x^{m+1} \left(-i b x^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-i b x^n\right)}{8 n}-\frac{3 i e^{-i a} x^{m+1} \left(i b x^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},i b x^n\right)}{8 n}-\frac{i e^{3 i a} 3^{-\frac{m+1}{n}} x^{m+1} \left(-i b x^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-3 i b x^n\right)}{8 n}+\frac{i e^{-3 i a} 3^{-\frac{m+1}{n}} x^{m+1} \left(i b x^n\right)^{-\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},3 i b x^n\right)}{8 n}",1,"((I/8)*x^(1 + m)*(3^((1 + m + n)/n)*E^((4*I)*a)*(I*b*x^n)^((1 + m)/n)*Gamma[(1 + m)/n, (-I)*b*x^n] - 3^((1 + m + n)/n)*E^((2*I)*a)*((-I)*b*x^n)^((1 + m)/n)*Gamma[(1 + m)/n, I*b*x^n] - E^((6*I)*a)*(I*b*x^n)^((1 + m)/n)*Gamma[(1 + m)/n, (-3*I)*b*x^n] + ((-I)*b*x^n)^((1 + m)/n)*Gamma[(1 + m)/n, (3*I)*b*x^n]))/(3^((1 + m)/n)*E^((3*I)*a)*n*(b^2*x^(2*n))^((1 + m)/n))","A",1
145,1,30,35,0.0747978,"\int x^{-1+2 n} \sin \left(a+b x^n\right) \, dx","Integrate[x^(-1 + 2*n)*Sin[a + b*x^n],x]","\frac{\sin \left(a+b x^n\right)-b x^n \cos \left(a+b x^n\right)}{b^2 n}","\frac{\sin \left(a+b x^n\right)}{b^2 n}-\frac{x^n \cos \left(a+b x^n\right)}{b n}",1,"(-(b*x^n*Cos[a + b*x^n]) + Sin[a + b*x^n])/(b^2*n)","A",1
146,1,29,34,0.0697903,"\int x^{-1+2 n} \cos \left(a+b x^n\right) \, dx","Integrate[x^(-1 + 2*n)*Cos[a + b*x^n],x]","\frac{b x^n \sin \left(a+b x^n\right)+\cos \left(a+b x^n\right)}{b^2 n}","\frac{\cos \left(a+b x^n\right)}{b^2 n}+\frac{x^n \sin \left(a+b x^n\right)}{b n}",1,"(Cos[a + b*x^n] + b*x^n*Sin[a + b*x^n])/(b^2*n)","A",1
147,1,47,46,0.0821132,"\int x^{-1-n} \sin \left(a+b x^n\right) \, dx","Integrate[x^(-1 - n)*Sin[a + b*x^n],x]","\frac{x^{-n} \left(b \cos (a) x^n \text{Ci}\left(b x^n\right)-b \sin (a) x^n \text{Si}\left(b x^n\right)-\sin \left(a+b x^n\right)\right)}{n}","\frac{b \cos (a) \text{Ci}\left(b x^n\right)}{n}-\frac{b \sin (a) \text{Si}\left(b x^n\right)}{n}-\frac{x^{-n} \sin \left(a+b x^n\right)}{n}",1,"(b*x^n*Cos[a]*CosIntegral[b*x^n] - Sin[a + b*x^n] - b*x^n*Sin[a]*SinIntegral[b*x^n])/(n*x^n)","A",1
148,1,58,67,0.1393699,"\int x^{-1-n} \sin ^2\left(a+b x^n\right) \, dx","Integrate[x^(-1 - n)*Sin[a + b*x^n]^2,x]","\frac{x^{-n} \left(2 b \sin (2 a) x^n \text{Ci}\left(2 b x^n\right)+2 b \cos (2 a) x^n \text{Si}\left(2 b x^n\right)+\cos \left(2 \left(a+b x^n\right)\right)-1\right)}{2 n}","\frac{b \sin (2 a) \text{Ci}\left(2 b x^n\right)}{n}+\frac{b \cos (2 a) \text{Si}\left(2 b x^n\right)}{n}+\frac{x^{-n} \cos \left(2 \left(a+b x^n\right)\right)}{2 n}-\frac{x^{-n}}{2 n}",1,"(-1 + Cos[2*(a + b*x^n)] + 2*b*x^n*CosIntegral[2*b*x^n]*Sin[2*a] + 2*b*x^n*Cos[2*a]*SinIntegral[2*b*x^n])/(2*n*x^n)","A",1
149,1,95,113,0.2048965,"\int x^{-1-n} \sin ^3\left(a+b x^n\right) \, dx","Integrate[x^(-1 - n)*Sin[a + b*x^n]^3,x]","\frac{x^{-n} \left(3 b \cos (a) x^n \text{Ci}\left(b x^n\right)-3 b \cos (3 a) x^n \text{Ci}\left(3 b x^n\right)-3 b \sin (a) x^n \text{Si}\left(b x^n\right)+3 b \sin (3 a) x^n \text{Si}\left(3 b x^n\right)-3 \sin \left(a+b x^n\right)+\sin \left(3 \left(a+b x^n\right)\right)\right)}{4 n}","\frac{3 b \cos (a) \text{Ci}\left(b x^n\right)}{4 n}-\frac{3 b \cos (3 a) \text{Ci}\left(3 b x^n\right)}{4 n}-\frac{3 b \sin (a) \text{Si}\left(b x^n\right)}{4 n}+\frac{3 b \sin (3 a) \text{Si}\left(3 b x^n\right)}{4 n}-\frac{3 x^{-n} \sin \left(a+b x^n\right)}{4 n}+\frac{x^{-n} \sin \left(3 \left(a+b x^n\right)\right)}{4 n}",1,"(3*b*x^n*Cos[a]*CosIntegral[b*x^n] - 3*b*x^n*Cos[3*a]*CosIntegral[3*b*x^n] - 3*Sin[a + b*x^n] + Sin[3*(a + b*x^n)] - 3*b*x^n*Sin[a]*SinIntegral[b*x^n] + 3*b*x^n*Sin[3*a]*SinIntegral[3*b*x^n])/(4*n*x^n)","A",1
150,1,68,78,0.1285369,"\int x^{-1-2 n} \sin \left(a+b x^n\right) \, dx","Integrate[x^(-1 - 2*n)*Sin[a + b*x^n],x]","-\frac{x^{-2 n} \left(b^2 \sin (a) x^{2 n} \text{Ci}\left(b x^n\right)+b^2 \cos (a) x^{2 n} \text{Si}\left(b x^n\right)+\sin \left(a+b x^n\right)+b x^n \cos \left(a+b x^n\right)\right)}{2 n}","-\frac{b^2 \sin (a) \text{Ci}\left(b x^n\right)}{2 n}-\frac{b^2 \cos (a) \text{Si}\left(b x^n\right)}{2 n}-\frac{x^{-2 n} \sin \left(a+b x^n\right)}{2 n}-\frac{b x^{-n} \cos \left(a+b x^n\right)}{2 n}",1,"-1/2*(b*x^n*Cos[a + b*x^n] + b^2*x^(2*n)*CosIntegral[b*x^n]*Sin[a] + Sin[a + b*x^n] + b^2*x^(2*n)*Cos[a]*SinIntegral[b*x^n])/(n*x^(2*n))","A",1
151,1,82,95,0.1765629,"\int x^{-1-2 n} \sin ^2\left(a+b x^n\right) \, dx","Integrate[x^(-1 - 2*n)*Sin[a + b*x^n]^2,x]","\frac{x^{-2 n} \left(4 b^2 \cos (2 a) x^{2 n} \text{Ci}\left(2 b x^n\right)-4 b^2 \sin (2 a) x^{2 n} \text{Si}\left(2 b x^n\right)-2 b x^n \sin \left(2 \left(a+b x^n\right)\right)+\cos \left(2 \left(a+b x^n\right)\right)-1\right)}{4 n}","\frac{b^2 \cos (2 a) \text{Ci}\left(2 b x^n\right)}{n}-\frac{b^2 \sin (2 a) \text{Si}\left(2 b x^n\right)}{n}-\frac{b x^{-n} \sin \left(2 \left(a+b x^n\right)\right)}{2 n}+\frac{x^{-2 n} \cos \left(2 \left(a+b x^n\right)\right)}{4 n}-\frac{x^{-2 n}}{4 n}",1,"(-1 + Cos[2*(a + b*x^n)] + 4*b^2*x^(2*n)*Cos[2*a]*CosIntegral[2*b*x^n] - 2*b*x^n*Sin[2*(a + b*x^n)] - 4*b^2*x^(2*n)*Sin[2*a]*SinIntegral[2*b*x^n])/(4*n*x^(2*n))","A",1
152,1,141,165,0.3028221,"\int x^{-1-2 n} \sin ^3\left(a+b x^n\right) \, dx","Integrate[x^(-1 - 2*n)*Sin[a + b*x^n]^3,x]","\frac{x^{-2 n} \left(-3 b^2 \sin (a) x^{2 n} \text{Ci}\left(b x^n\right)+9 b^2 \sin (3 a) x^{2 n} \text{Ci}\left(3 b x^n\right)-3 b^2 \cos (a) x^{2 n} \text{Si}\left(b x^n\right)+9 b^2 \cos (3 a) x^{2 n} \text{Si}\left(3 b x^n\right)-3 \sin \left(a+b x^n\right)+\sin \left(3 \left(a+b x^n\right)\right)-3 b x^n \cos \left(a+b x^n\right)+3 b x^n \cos \left(3 \left(a+b x^n\right)\right)\right)}{8 n}","-\frac{3 b^2 \sin (a) \text{Ci}\left(b x^n\right)}{8 n}+\frac{9 b^2 \sin (3 a) \text{Ci}\left(3 b x^n\right)}{8 n}-\frac{3 b^2 \cos (a) \text{Si}\left(b x^n\right)}{8 n}+\frac{9 b^2 \cos (3 a) \text{Si}\left(3 b x^n\right)}{8 n}-\frac{3 x^{-2 n} \sin \left(a+b x^n\right)}{8 n}+\frac{x^{-2 n} \sin \left(3 \left(a+b x^n\right)\right)}{8 n}-\frac{3 b x^{-n} \cos \left(a+b x^n\right)}{8 n}+\frac{3 b x^{-n} \cos \left(3 \left(a+b x^n\right)\right)}{8 n}",1,"(-3*b*x^n*Cos[a + b*x^n] + 3*b*x^n*Cos[3*(a + b*x^n)] - 3*b^2*x^(2*n)*CosIntegral[b*x^n]*Sin[a] + 9*b^2*x^(2*n)*CosIntegral[3*b*x^n]*Sin[3*a] - 3*Sin[a + b*x^n] + Sin[3*(a + b*x^n)] - 3*b^2*x^(2*n)*Cos[a]*SinIntegral[b*x^n] + 9*b^2*x^(2*n)*Cos[3*a]*SinIntegral[3*b*x^n])/(8*n*x^(2*n))","A",1
153,1,173,223,1.0835851,"\int (e+f x)^3 \sin \left(b (c+d x)^2\right) \, dx","Integrate[(e + f*x)^3*Sin[b*(c + d*x)^2],x]","\frac{4 \sqrt{2 \pi } b^{3/2} (d e-c f)^3 S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} (c+d x)\right)-4 b f \cos \left(b (c+d x)^2\right) \left(c^2 f^2-c d f (3 e+f x)+d^2 \left(3 e^2+3 e f x+f^2 x^2\right)\right)-6 \sqrt{2 \pi } \sqrt{b} f^2 (c f-d e) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} (c+d x)\right)+4 f^3 \sin \left(b (c+d x)^2\right)}{8 b^2 d^4}","\frac{3 \sqrt{\frac{\pi }{2}} f^2 (d e-c f) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} (c+d x)\right)}{2 b^{3/2} d^4}+\frac{f^3 \sin \left(b (c+d x)^2\right)}{2 b^2 d^4}-\frac{3 f^2 (c+d x) (d e-c f) \cos \left(b (c+d x)^2\right)}{2 b d^4}+\frac{\sqrt{\frac{\pi }{2}} (d e-c f)^3 S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} (c+d x)\right)}{\sqrt{b} d^4}-\frac{3 f (d e-c f)^2 \cos \left(b (c+d x)^2\right)}{2 b d^4}-\frac{f^3 (c+d x)^2 \cos \left(b (c+d x)^2\right)}{2 b d^4}",1,"(-4*b*f*(c^2*f^2 - c*d*f*(3*e + f*x) + d^2*(3*e^2 + 3*e*f*x + f^2*x^2))*Cos[b*(c + d*x)^2] - 6*Sqrt[b]*f^2*(-(d*e) + c*f)*Sqrt[2*Pi]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)] + 4*b^(3/2)*(d*e - c*f)^3*Sqrt[2*Pi]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)] + 4*f^3*Sin[b*(c + d*x)^2])/(8*b^2*d^4)","A",1
154,1,117,150,0.647448,"\int (e+f x)^2 \sin \left(b (c+d x)^2\right) \, dx","Integrate[(e + f*x)^2*Sin[b*(c + d*x)^2],x]","\frac{2 \sqrt{2 \pi } b (d e-c f)^2 S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} (c+d x)\right)-2 \sqrt{b} f \cos \left(b (c+d x)^2\right) (-c f+2 d e+d f x)+\sqrt{2 \pi } f^2 C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} (c+d x)\right)}{4 b^{3/2} d^3}","\frac{\sqrt{\frac{\pi }{2}} f^2 C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} (c+d x)\right)}{2 b^{3/2} d^3}+\frac{\sqrt{\frac{\pi }{2}} (d e-c f)^2 S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} (c+d x)\right)}{\sqrt{b} d^3}-\frac{f (d e-c f) \cos \left(b (c+d x)^2\right)}{b d^3}-\frac{f^2 (c+d x) \cos \left(b (c+d x)^2\right)}{2 b d^3}",1,"(-2*Sqrt[b]*f*(2*d*e - c*f + d*f*x)*Cos[b*(c + d*x)^2] + f^2*Sqrt[2*Pi]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)] + 2*b*(d*e - c*f)^2*Sqrt[2*Pi]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)])/(4*b^(3/2)*d^3)","A",1
155,1,66,69,0.1883585,"\int (e+f x) \sin \left(b (c+d x)^2\right) \, dx","Integrate[(e + f*x)*Sin[b*(c + d*x)^2],x]","\frac{\sqrt{2 \pi } \sqrt{b} (d e-c f) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} (c+d x)\right)-f \cos \left(b (c+d x)^2\right)}{2 b d^2}","\frac{\sqrt{\frac{\pi }{2}} (d e-c f) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} (c+d x)\right)}{\sqrt{b} d^2}-\frac{f \cos \left(b (c+d x)^2\right)}{2 b d^2}",1,"(-(f*Cos[b*(c + d*x)^2]) + Sqrt[b]*(d*e - c*f)*Sqrt[2*Pi]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)])/(2*b*d^2)","A",1
156,1,39,39,0.0152797,"\int \sin \left(b (c+d x)^2\right) \, dx","Integrate[Sin[b*(c + d*x)^2],x]","\frac{\sqrt{\frac{\pi }{2}} S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} (c+d x)\right)}{\sqrt{b} d}","\frac{\sqrt{\frac{\pi }{2}} S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} (c+d x)\right)}{\sqrt{b} d}",1,"(Sqrt[Pi/2]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)])/(Sqrt[b]*d)","A",1
157,0,0,21,5.3187967,"\int \frac{\sin \left(b (c+d x)^2\right)}{e+f x} \, dx","Integrate[Sin[b*(c + d*x)^2]/(e + f*x),x]","\int \frac{\sin \left(b (c+d x)^2\right)}{e+f x} \, dx","\text{Int}\left(\frac{\sin \left(b (c+d x)^2\right)}{e+f x},x\right)",0,"Integrate[Sin[b*(c + d*x)^2]/(e + f*x), x]","A",-1
158,0,0,21,10.0131595,"\int \frac{\sin \left(b (c+d x)^2\right)}{(e+f x)^2} \, dx","Integrate[Sin[b*(c + d*x)^2]/(e + f*x)^2,x]","\int \frac{\sin \left(b (c+d x)^2\right)}{(e+f x)^2} \, dx","\text{Int}\left(\frac{\sin \left(b (c+d x)^2\right)}{(e+f x)^2},x\right)",0,"Integrate[Sin[b*(c + d*x)^2]/(e + f*x)^2, x]","A",-1
159,1,440,337,0.9340632,"\int (e+f x)^3 \sin \left(\frac{b}{(c+d x)^2}\right) \, dx","Integrate[(e + f*x)^3*Sin[b/(c + d*x)^2],x]","\frac{8 \sqrt{2 \pi } b^{3/2} d e f^2 S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{c+d x}\right)-8 \sqrt{2 \pi } b^{3/2} c f^3 S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{c+d x}\right)+b^2 f^3 \text{Si}\left(\frac{b}{(c+d x)^2}\right)+c^4 \left(-f^3\right) \sin \left(\frac{b}{(c+d x)^2}\right)+4 c^3 d e f^2 \sin \left(\frac{b}{(c+d x)^2}\right)-6 c^2 d^2 e^2 f \sin \left(\frac{b}{(c+d x)^2}\right)-7 b c^2 f^3 \cos \left(\frac{b}{(c+d x)^2}\right)-6 b f (d e-c f)^2 \text{Ci}\left(\frac{b}{(c+d x)^2}\right)+4 d^4 e^3 x \sin \left(\frac{b}{(c+d x)^2}\right)+6 d^4 e^2 f x^2 \sin \left(\frac{b}{(c+d x)^2}\right)+4 d^4 e f^2 x^3 \sin \left(\frac{b}{(c+d x)^2}\right)+d^4 f^3 x^4 \sin \left(\frac{b}{(c+d x)^2}\right)+4 c d^3 e^3 \sin \left(\frac{b}{(c+d x)^2}\right)+8 b d^2 e f^2 x \cos \left(\frac{b}{(c+d x)^2}\right)+b d^2 f^3 x^2 \cos \left(\frac{b}{(c+d x)^2}\right)+8 b c d e f^2 \cos \left(\frac{b}{(c+d x)^2}\right)-4 \sqrt{2 \pi } \sqrt{b} (d e-c f)^3 C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{c+d x}\right)-6 b c d f^3 x \cos \left(\frac{b}{(c+d x)^2}\right)}{4 d^4}","\frac{2 \sqrt{2 \pi } b^{3/2} f^2 (d e-c f) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{c+d x}\right)}{d^4}+\frac{b^2 f^3 \text{Si}\left(\frac{b}{(c+d x)^2}\right)}{4 d^4}-\frac{3 b f (d e-c f)^2 \text{Ci}\left(\frac{b}{(c+d x)^2}\right)}{2 d^4}+\frac{f^2 (c+d x)^3 (d e-c f) \sin \left(\frac{b}{(c+d x)^2}\right)}{d^4}+\frac{2 b f^2 (c+d x) (d e-c f) \cos \left(\frac{b}{(c+d x)^2}\right)}{d^4}-\frac{\sqrt{2 \pi } \sqrt{b} (d e-c f)^3 C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{c+d x}\right)}{d^4}+\frac{3 f (c+d x)^2 (d e-c f)^2 \sin \left(\frac{b}{(c+d x)^2}\right)}{2 d^4}+\frac{(c+d x) (d e-c f)^3 \sin \left(\frac{b}{(c+d x)^2}\right)}{d^4}+\frac{f^3 (c+d x)^4 \sin \left(\frac{b}{(c+d x)^2}\right)}{4 d^4}+\frac{b f^3 (c+d x)^2 \cos \left(\frac{b}{(c+d x)^2}\right)}{4 d^4}",1,"(8*b*c*d*e*f^2*Cos[b/(c + d*x)^2] - 7*b*c^2*f^3*Cos[b/(c + d*x)^2] + 8*b*d^2*e*f^2*x*Cos[b/(c + d*x)^2] - 6*b*c*d*f^3*x*Cos[b/(c + d*x)^2] + b*d^2*f^3*x^2*Cos[b/(c + d*x)^2] - 6*b*f*(d*e - c*f)^2*CosIntegral[b/(c + d*x)^2] - 4*Sqrt[b]*(d*e - c*f)^3*Sqrt[2*Pi]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)] + 8*b^(3/2)*d*e*f^2*Sqrt[2*Pi]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)] - 8*b^(3/2)*c*f^3*Sqrt[2*Pi]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)] + 4*c*d^3*e^3*Sin[b/(c + d*x)^2] - 6*c^2*d^2*e^2*f*Sin[b/(c + d*x)^2] + 4*c^3*d*e*f^2*Sin[b/(c + d*x)^2] - c^4*f^3*Sin[b/(c + d*x)^2] + 4*d^4*e^3*x*Sin[b/(c + d*x)^2] + 6*d^4*e^2*f*x^2*Sin[b/(c + d*x)^2] + 4*d^4*e*f^2*x^3*Sin[b/(c + d*x)^2] + d^4*f^3*x^4*Sin[b/(c + d*x)^2] + b^2*f^3*SinIntegral[b/(c + d*x)^2])/(4*d^4)","A",1
160,1,265,233,0.5083534,"\int (e+f x)^2 \sin \left(\frac{b}{(c+d x)^2}\right) \, dx","Integrate[(e + f*x)^2*Sin[b/(c + d*x)^2],x]","\frac{2 \sqrt{2 \pi } b^{3/2} f^2 S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{c+d x}\right)+c^3 f^2 \sin \left(\frac{b}{(c+d x)^2}\right)-3 c^2 d e f \sin \left(\frac{b}{(c+d x)^2}\right)+3 b f (c f-d e) \text{Ci}\left(\frac{b}{(c+d x)^2}\right)+3 d^3 e^2 x \sin \left(\frac{b}{(c+d x)^2}\right)+3 d^3 e f x^2 \sin \left(\frac{b}{(c+d x)^2}\right)+d^3 f^2 x^3 \sin \left(\frac{b}{(c+d x)^2}\right)+3 c d^2 e^2 \sin \left(\frac{b}{(c+d x)^2}\right)-3 \sqrt{2 \pi } \sqrt{b} (d e-c f)^2 C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{c+d x}\right)+2 b c f^2 \cos \left(\frac{b}{(c+d x)^2}\right)+2 b d f^2 x \cos \left(\frac{b}{(c+d x)^2}\right)}{3 d^3}","\frac{2 \sqrt{2 \pi } b^{3/2} f^2 S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{c+d x}\right)}{3 d^3}-\frac{b f (d e-c f) \text{Ci}\left(\frac{b}{(c+d x)^2}\right)}{d^3}-\frac{\sqrt{2 \pi } \sqrt{b} (d e-c f)^2 C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{c+d x}\right)}{d^3}+\frac{f (c+d x)^2 (d e-c f) \sin \left(\frac{b}{(c+d x)^2}\right)}{d^3}+\frac{(c+d x) (d e-c f)^2 \sin \left(\frac{b}{(c+d x)^2}\right)}{d^3}+\frac{f^2 (c+d x)^3 \sin \left(\frac{b}{(c+d x)^2}\right)}{3 d^3}+\frac{2 b f^2 (c+d x) \cos \left(\frac{b}{(c+d x)^2}\right)}{3 d^3}",1,"(2*b*c*f^2*Cos[b/(c + d*x)^2] + 2*b*d*f^2*x*Cos[b/(c + d*x)^2] + 3*b*f*(-(d*e) + c*f)*CosIntegral[b/(c + d*x)^2] - 3*Sqrt[b]*(d*e - c*f)^2*Sqrt[2*Pi]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)] + 2*b^(3/2)*f^2*Sqrt[2*Pi]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)] + 3*c*d^2*e^2*Sin[b/(c + d*x)^2] - 3*c^2*d*e*f*Sin[b/(c + d*x)^2] + c^3*f^2*Sin[b/(c + d*x)^2] + 3*d^3*e^2*x*Sin[b/(c + d*x)^2] + 3*d^3*e*f*x^2*Sin[b/(c + d*x)^2] + d^3*f^2*x^3*Sin[b/(c + d*x)^2])/(3*d^3)","A",1
161,1,95,120,0.2871225,"\int (e+f x) \sin \left(\frac{b}{(c+d x)^2}\right) \, dx","Integrate[(e + f*x)*Sin[b/(c + d*x)^2],x]","-\frac{b f \text{Ci}\left(\frac{b}{(c+d x)^2}\right)+2 \sqrt{2 \pi } \sqrt{b} (d e-c f) C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{c+d x}\right)+(c+d x) \sin \left(\frac{b}{(c+d x)^2}\right) (c f-2 d e-d f x)}{2 d^2}","-\frac{b f \text{Ci}\left(\frac{b}{(c+d x)^2}\right)}{2 d^2}-\frac{\sqrt{2 \pi } \sqrt{b} (d e-c f) C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{c+d x}\right)}{d^2}+\frac{(c+d x) (d e-c f) \sin \left(\frac{b}{(c+d x)^2}\right)}{d^2}+\frac{f (c+d x)^2 \sin \left(\frac{b}{(c+d x)^2}\right)}{2 d^2}",1,"-1/2*(b*f*CosIntegral[b/(c + d*x)^2] + 2*Sqrt[b]*(d*e - c*f)*Sqrt[2*Pi]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)] + (c + d*x)*(-2*d*e + c*f - d*f*x)*Sin[b/(c + d*x)^2])/d^2","A",1
162,1,60,60,0.0341294,"\int \sin \left(\frac{b}{(c+d x)^2}\right) \, dx","Integrate[Sin[b/(c + d*x)^2],x]","\frac{(c+d x) \sin \left(\frac{b}{(c+d x)^2}\right)}{d}-\frac{\sqrt{2 \pi } \sqrt{b} C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{c+d x}\right)}{d}","\frac{(c+d x) \sin \left(\frac{b}{(c+d x)^2}\right)}{d}-\frac{\sqrt{2 \pi } \sqrt{b} C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{c+d x}\right)}{d}",1,"-((Sqrt[b]*Sqrt[2*Pi]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)])/d) + ((c + d*x)*Sin[b/(c + d*x)^2])/d","A",1
163,0,0,21,1.558688,"\int \frac{\sin \left(\frac{b}{(c+d x)^2}\right)}{e+f x} \, dx","Integrate[Sin[b/(c + d*x)^2]/(e + f*x),x]","\int \frac{\sin \left(\frac{b}{(c+d x)^2}\right)}{e+f x} \, dx","\text{Int}\left(\frac{\sin \left(\frac{b}{(c+d x)^2}\right)}{e+f x},x\right)",0,"Integrate[Sin[b/(c + d*x)^2]/(e + f*x), x]","A",-1
164,0,0,21,19.8886387,"\int \frac{\sin \left(\frac{b}{(c+d x)^2}\right)}{(e+f x)^2} \, dx","Integrate[Sin[b/(c + d*x)^2]/(e + f*x)^2,x]","\int \frac{\sin \left(\frac{b}{(c+d x)^2}\right)}{(e+f x)^2} \, dx","\text{Int}\left(\frac{\sin \left(\frac{b}{(c+d x)^2}\right)}{(e+f x)^2},x\right)",0,"Integrate[Sin[b/(c + d*x)^2]/(e + f*x)^2, x]","A",-1
165,1,218,341,3.0321997,"\int (e+f x)^3 \sin \left(a+b (c+d x)^2\right) \, dx","Integrate[(e + f*x)^3*Sin[a + b*(c + d*x)^2],x]","\frac{-4 b f \left(c^2 f^2-c d f (3 e+f x)+d^2 \left(3 e^2+3 e f x+f^2 x^2\right)\right) \cos \left(a+b (c+d x)^2\right)+2 \sqrt{2 \pi } \sqrt{b} (d e-c f) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} (c+d x)\right) \left(2 b \sin (a) (d e-c f)^2+3 f^2 \cos (a)\right)+2 \sqrt{2 \pi } \sqrt{b} (d e-c f) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} (c+d x)\right) \left(2 b \cos (a) (d e-c f)^2-3 f^2 \sin (a)\right)+4 f^3 \sin \left(a+b (c+d x)^2\right)}{8 b^2 d^4}","\frac{3 \sqrt{\frac{\pi }{2}} f^2 \cos (a) (d e-c f) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} (c+d x)\right)}{2 b^{3/2} d^4}-\frac{3 \sqrt{\frac{\pi }{2}} f^2 \sin (a) (d e-c f) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} (c+d x)\right)}{2 b^{3/2} d^4}+\frac{f^3 \sin \left(a+b (c+d x)^2\right)}{2 b^2 d^4}-\frac{3 f^2 (c+d x) (d e-c f) \cos \left(a+b (c+d x)^2\right)}{2 b d^4}+\frac{\sqrt{\frac{\pi }{2}} \sin (a) (d e-c f)^3 C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} (c+d x)\right)}{\sqrt{b} d^4}+\frac{\sqrt{\frac{\pi }{2}} \cos (a) (d e-c f)^3 S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} (c+d x)\right)}{\sqrt{b} d^4}-\frac{3 f (d e-c f)^2 \cos \left(a+b (c+d x)^2\right)}{2 b d^4}-\frac{f^3 (c+d x)^2 \cos \left(a+b (c+d x)^2\right)}{2 b d^4}",1,"(-4*b*f*(c^2*f^2 - c*d*f*(3*e + f*x) + d^2*(3*e^2 + 3*e*f*x + f^2*x^2))*Cos[a + b*(c + d*x)^2] + 2*Sqrt[b]*(d*e - c*f)*Sqrt[2*Pi]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)]*(2*b*(d*e - c*f)^2*Cos[a] - 3*f^2*Sin[a]) + 2*Sqrt[b]*(d*e - c*f)*Sqrt[2*Pi]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)]*(3*f^2*Cos[a] + 2*b*(d*e - c*f)^2*Sin[a]) + 4*f^3*Sin[a + b*(c + d*x)^2])/(8*b^2*d^4)","A",1
166,1,151,256,1.8345409,"\int (e+f x)^2 \sin \left(a+b (c+d x)^2\right) \, dx","Integrate[(e + f*x)^2*Sin[a + b*(c + d*x)^2],x]","\frac{2 \sqrt{2 \pi } C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} (c+d x)\right) \left(2 b \sin (a) (d e-c f)^2+f^2 \cos (a)\right)+2 \sqrt{2 \pi } S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} (c+d x)\right) \left(2 b \cos (a) (d e-c f)^2-f^2 \sin (a)\right)-4 \sqrt{b} f (-c f+2 d e+d f x) \cos \left(a+b (c+d x)^2\right)}{8 b^{3/2} d^3}","\frac{\sqrt{\frac{\pi }{2}} f^2 \cos (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} (c+d x)\right)}{2 b^{3/2} d^3}-\frac{\sqrt{\frac{\pi }{2}} f^2 \sin (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} (c+d x)\right)}{2 b^{3/2} d^3}+\frac{\sqrt{\frac{\pi }{2}} \sin (a) (d e-c f)^2 C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} (c+d x)\right)}{\sqrt{b} d^3}+\frac{\sqrt{\frac{\pi }{2}} \cos (a) (d e-c f)^2 S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} (c+d x)\right)}{\sqrt{b} d^3}-\frac{f (d e-c f) \cos \left(a+b (c+d x)^2\right)}{b d^3}-\frac{f^2 (c+d x) \cos \left(a+b (c+d x)^2\right)}{2 b d^3}",1,"(-4*Sqrt[b]*f*(2*d*e - c*f + d*f*x)*Cos[a + b*(c + d*x)^2] + 2*Sqrt[2*Pi]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)]*(2*b*(d*e - c*f)^2*Cos[a] - f^2*Sin[a]) + 2*Sqrt[2*Pi]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)]*(f^2*Cos[a] + 2*b*(d*e - c*f)^2*Sin[a]))/(8*b^(3/2)*d^3)","A",1
167,1,114,122,0.6042139,"\int (e+f x) \sin \left(a+b (c+d x)^2\right) \, dx","Integrate[(e + f*x)*Sin[a + b*(c + d*x)^2],x]","\frac{\sqrt{2 \pi } \sqrt{b} \sin (a) (d e-c f) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} (c+d x)\right)+\sqrt{2 \pi } \sqrt{b} \cos (a) (d e-c f) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} (c+d x)\right)-f \cos \left(a+b (c+d x)^2\right)}{2 b d^2}","\frac{\sqrt{\frac{\pi }{2}} \sin (a) (d e-c f) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} (c+d x)\right)}{\sqrt{b} d^2}+\frac{\sqrt{\frac{\pi }{2}} \cos (a) (d e-c f) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} (c+d x)\right)}{\sqrt{b} d^2}-\frac{f \cos \left(a+b (c+d x)^2\right)}{2 b d^2}",1,"(-(f*Cos[a + b*(c + d*x)^2]) + Sqrt[b]*(d*e - c*f)*Sqrt[2*Pi]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)] + Sqrt[b]*(d*e - c*f)*Sqrt[2*Pi]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)]*Sin[a])/(2*b*d^2)","A",1
168,1,67,83,0.0683697,"\int \sin \left(a+b (c+d x)^2\right) \, dx","Integrate[Sin[a + b*(c + d*x)^2],x]","\frac{\sqrt{\frac{\pi }{2}} \left(\sin (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} (c+d x)\right)+\cos (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} (c+d x)\right)\right)}{\sqrt{b} d}","\frac{\sqrt{\frac{\pi }{2}} \sin (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} (c+d x)\right)}{\sqrt{b} d}+\frac{\sqrt{\frac{\pi }{2}} \cos (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} (c+d x)\right)}{\sqrt{b} d}",1,"(Sqrt[Pi/2]*(Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)] + FresnelC[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)]*Sin[a]))/(Sqrt[b]*d)","A",1
169,0,0,23,15.1173187,"\int \frac{\sin \left(a+b (c+d x)^2\right)}{e+f x} \, dx","Integrate[Sin[a + b*(c + d*x)^2]/(e + f*x),x]","\int \frac{\sin \left(a+b (c+d x)^2\right)}{e+f x} \, dx","\text{Int}\left(\frac{\sin \left(a+b (c+d x)^2\right)}{e+f x},x\right)",0,"Integrate[Sin[a + b*(c + d*x)^2]/(e + f*x), x]","A",-1
170,0,0,23,25.6122745,"\int \frac{\sin \left(a+b (c+d x)^2\right)}{(e+f x)^2} \, dx","Integrate[Sin[a + b*(c + d*x)^2]/(e + f*x)^2,x]","\int \frac{\sin \left(a+b (c+d x)^2\right)}{(e+f x)^2} \, dx","\text{Int}\left(\frac{\sin \left(a+b (c+d x)^2\right)}{(e+f x)^2},x\right)",0,"Integrate[Sin[a + b*(c + d*x)^2]/(e + f*x)^2, x]","A",-1
171,0,0,434,132.799901,"\int (e+f x)^3 \sin \left(a+b (c+d x)^3\right) \, dx","Integrate[(e + f*x)^3*Sin[a + b*(c + d*x)^3],x]","\int (e+f x)^3 \sin \left(a+b (c+d x)^3\right) \, dx","-\frac{f^2 (d e-c f) \cos \left(a+b (c+d x)^3\right)}{b d^4}+\frac{i e^{i a} f (c+d x)^2 (d e-c f)^2 \Gamma \left(\frac{2}{3},-i b (c+d x)^3\right)}{2 d^4 \left(-i b (c+d x)^3\right)^{2/3}}-\frac{i e^{-i a} f (c+d x)^2 (d e-c f)^2 \Gamma \left(\frac{2}{3},i b (c+d x)^3\right)}{2 d^4 \left(i b (c+d x)^3\right)^{2/3}}+\frac{i e^{i a} (c+d x) (d e-c f)^3 \Gamma \left(\frac{1}{3},-i b (c+d x)^3\right)}{6 d^4 \sqrt[3]{-i b (c+d x)^3}}-\frac{i e^{-i a} (c+d x) (d e-c f)^3 \Gamma \left(\frac{1}{3},i b (c+d x)^3\right)}{6 d^4 \sqrt[3]{i b (c+d x)^3}}-\frac{f^3 (c+d x) \cos \left(a+b (c+d x)^3\right)}{3 b d^4}-\frac{e^{i a} f^3 (c+d x) \Gamma \left(\frac{1}{3},-i b (c+d x)^3\right)}{18 b d^4 \sqrt[3]{-i b (c+d x)^3}}-\frac{e^{-i a} f^3 (c+d x) \Gamma \left(\frac{1}{3},i b (c+d x)^3\right)}{18 b d^4 \sqrt[3]{i b (c+d x)^3}}",1,"Integrate[(e + f*x)^3*Sin[a + b*(c + d*x)^3], x]","F",-1
172,0,0,280,53.0405657,"\int (e+f x)^2 \sin \left(a+b (c+d x)^3\right) \, dx","Integrate[(e + f*x)^2*Sin[a + b*(c + d*x)^3],x]","\int (e+f x)^2 \sin \left(a+b (c+d x)^3\right) \, dx","\frac{i e^{i a} f (c+d x)^2 (d e-c f) \Gamma \left(\frac{2}{3},-i b (c+d x)^3\right)}{3 d^3 \left(-i b (c+d x)^3\right)^{2/3}}-\frac{i e^{-i a} f (c+d x)^2 (d e-c f) \Gamma \left(\frac{2}{3},i b (c+d x)^3\right)}{3 d^3 \left(i b (c+d x)^3\right)^{2/3}}+\frac{i e^{i a} (c+d x) (d e-c f)^2 \Gamma \left(\frac{1}{3},-i b (c+d x)^3\right)}{6 d^3 \sqrt[3]{-i b (c+d x)^3}}-\frac{i e^{-i a} (c+d x) (d e-c f)^2 \Gamma \left(\frac{1}{3},i b (c+d x)^3\right)}{6 d^3 \sqrt[3]{i b (c+d x)^3}}-\frac{f^2 \cos \left(a+b (c+d x)^3\right)}{3 b d^3}",1,"Integrate[(e + f*x)^2*Sin[a + b*(c + d*x)^3], x]","F",-1
173,0,0,235,46.0080562,"\int (e+f x) \sin \left(a+b (c+d x)^3\right) \, dx","Integrate[(e + f*x)*Sin[a + b*(c + d*x)^3],x]","\int (e+f x) \sin \left(a+b (c+d x)^3\right) \, dx","\frac{i e^{i a} (c+d x) (d e-c f) \Gamma \left(\frac{1}{3},-i b (c+d x)^3\right)}{6 d^2 \sqrt[3]{-i b (c+d x)^3}}-\frac{i e^{-i a} (c+d x) (d e-c f) \Gamma \left(\frac{1}{3},i b (c+d x)^3\right)}{6 d^2 \sqrt[3]{i b (c+d x)^3}}+\frac{i e^{i a} f (c+d x)^2 \Gamma \left(\frac{2}{3},-i b (c+d x)^3\right)}{6 d^2 \left(-i b (c+d x)^3\right)^{2/3}}-\frac{i e^{-i a} f (c+d x)^2 \Gamma \left(\frac{2}{3},i b (c+d x)^3\right)}{6 d^2 \left(i b (c+d x)^3\right)^{2/3}}",1,"Integrate[(e + f*x)*Sin[a + b*(c + d*x)^3], x]","F",-1
174,1,115,107,0.0202579,"\int \sin \left(a+b (c+d x)^3\right) \, dx","Integrate[Sin[a + b*(c + d*x)^3],x]","\frac{i (c+d x) \left((\cos (a)+i \sin (a)) \sqrt[3]{i b (c+d x)^3} \Gamma \left(\frac{1}{3},-i b (c+d x)^3\right)-(\cos (a)-i \sin (a)) \sqrt[3]{-i b (c+d x)^3} \Gamma \left(\frac{1}{3},i b (c+d x)^3\right)\right)}{6 d \sqrt[3]{b^2 (c+d x)^6}}","\frac{i e^{i a} (c+d x) \Gamma \left(\frac{1}{3},-i b (c+d x)^3\right)}{6 d \sqrt[3]{-i b (c+d x)^3}}-\frac{i e^{-i a} (c+d x) \Gamma \left(\frac{1}{3},i b (c+d x)^3\right)}{6 d \sqrt[3]{i b (c+d x)^3}}",1,"((I/6)*(c + d*x)*(-(((-I)*b*(c + d*x)^3)^(1/3)*Gamma[1/3, I*b*(c + d*x)^3]*(Cos[a] - I*Sin[a])) + (I*b*(c + d*x)^3)^(1/3)*Gamma[1/3, (-I)*b*(c + d*x)^3]*(Cos[a] + I*Sin[a])))/(d*(b^2*(c + d*x)^6)^(1/3))","A",1
175,0,0,23,63.0391307,"\int \frac{\sin \left(a+b (c+d x)^3\right)}{e+f x} \, dx","Integrate[Sin[a + b*(c + d*x)^3]/(e + f*x),x]","\int \frac{\sin \left(a+b (c+d x)^3\right)}{e+f x} \, dx","\text{Int}\left(\frac{\sin \left(a+b (c+d x)^3\right)}{e+f x},x\right)",0,"Integrate[Sin[a + b*(c + d*x)^3]/(e + f*x), x]","A",-1
176,0,0,23,130.6452806,"\int \frac{\sin \left(a+b (c+d x)^3\right)}{(e+f x)^2} \, dx","Integrate[Sin[a + b*(c + d*x)^3]/(e + f*x)^2,x]","\int \frac{\sin \left(a+b (c+d x)^3\right)}{(e+f x)^2} \, dx","\text{Int}\left(\frac{\sin \left(a+b (c+d x)^3\right)}{(e+f x)^2},x\right)",0,"Integrate[Sin[a + b*(c + d*x)^3]/(e + f*x)^2, x]","A",-1
177,1,467,371,1.5405118,"\int (e+f x)^2 \sin \left(a+\frac{b}{(c+d x)^2}\right) \, dx","Integrate[(e + f*x)^2*Sin[a + b/(c + d*x)^2],x]","\frac{2 \sqrt{2 \pi } b^{3/2} f^2 \cos (a) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{c+d x}\right)+c^3 f^2 \sin \left(a+\frac{b}{(c+d x)^2}\right)-3 c^2 d e f \sin \left(a+\frac{b}{(c+d x)^2}\right)+3 \sqrt{2 \pi } \sqrt{b} c^2 f^2 \sin (a) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{c+d x}\right)+3 b f \cos (a) (c f-d e) \text{Ci}\left(\frac{b}{(c+d x)^2}\right)+3 d^3 e^2 x \sin \left(a+\frac{b}{(c+d x)^2}\right)+3 d^3 e f x^2 \sin \left(a+\frac{b}{(c+d x)^2}\right)+d^3 f^2 x^3 \sin \left(a+\frac{b}{(c+d x)^2}\right)+3 \sqrt{2 \pi } \sqrt{b} d^2 e^2 \sin (a) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{c+d x}\right)+3 c d^2 e^2 \sin \left(a+\frac{b}{(c+d x)^2}\right)+\sqrt{2 \pi } \sqrt{b} C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{c+d x}\right) \left(2 b f^2 \sin (a)-3 \cos (a) (d e-c f)^2\right)-6 \sqrt{2 \pi } \sqrt{b} c d e f \sin (a) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{c+d x}\right)+3 b d e f \sin (a) \text{Si}\left(\frac{b}{(c+d x)^2}\right)-3 b c f^2 \sin (a) \text{Si}\left(\frac{b}{(c+d x)^2}\right)+2 b c f^2 \cos \left(a+\frac{b}{(c+d x)^2}\right)+2 b d f^2 x \cos \left(a+\frac{b}{(c+d x)^2}\right)}{3 d^3}","\frac{2 \sqrt{2 \pi } b^{3/2} f^2 \sin (a) C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{c+d x}\right)}{3 d^3}+\frac{2 \sqrt{2 \pi } b^{3/2} f^2 \cos (a) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{c+d x}\right)}{3 d^3}-\frac{b f \cos (a) (d e-c f) \text{Ci}\left(\frac{b}{(c+d x)^2}\right)}{d^3}-\frac{\sqrt{2 \pi } \sqrt{b} \cos (a) (d e-c f)^2 C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{c+d x}\right)}{d^3}+\frac{\sqrt{2 \pi } \sqrt{b} \sin (a) (d e-c f)^2 S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{c+d x}\right)}{d^3}+\frac{b f \sin (a) (d e-c f) \text{Si}\left(\frac{b}{(c+d x)^2}\right)}{d^3}+\frac{f (c+d x)^2 (d e-c f) \sin \left(a+\frac{b}{(c+d x)^2}\right)}{d^3}+\frac{(c+d x) (d e-c f)^2 \sin \left(a+\frac{b}{(c+d x)^2}\right)}{d^3}+\frac{f^2 (c+d x)^3 \sin \left(a+\frac{b}{(c+d x)^2}\right)}{3 d^3}+\frac{2 b f^2 (c+d x) \cos \left(a+\frac{b}{(c+d x)^2}\right)}{3 d^3}",1,"(2*b*c*f^2*Cos[a + b/(c + d*x)^2] + 2*b*d*f^2*x*Cos[a + b/(c + d*x)^2] + 3*b*f*(-(d*e) + c*f)*Cos[a]*CosIntegral[b/(c + d*x)^2] + 2*b^(3/2)*f^2*Sqrt[2*Pi]*Cos[a]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)] + 3*Sqrt[b]*d^2*e^2*Sqrt[2*Pi]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)]*Sin[a] - 6*Sqrt[b]*c*d*e*f*Sqrt[2*Pi]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)]*Sin[a] + 3*Sqrt[b]*c^2*f^2*Sqrt[2*Pi]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)]*Sin[a] + Sqrt[b]*Sqrt[2*Pi]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)]*(-3*(d*e - c*f)^2*Cos[a] + 2*b*f^2*Sin[a]) + 3*c*d^2*e^2*Sin[a + b/(c + d*x)^2] - 3*c^2*d*e*f*Sin[a + b/(c + d*x)^2] + c^3*f^2*Sin[a + b/(c + d*x)^2] + 3*d^3*e^2*x*Sin[a + b/(c + d*x)^2] + 3*d^3*e*f*x^2*Sin[a + b/(c + d*x)^2] + d^3*f^2*x^3*Sin[a + b/(c + d*x)^2] + 3*b*d*e*f*Sin[a]*SinIntegral[b/(c + d*x)^2] - 3*b*c*f^2*Sin[a]*SinIntegral[b/(c + d*x)^2])/(3*d^3)","A",1
178,1,242,198,0.79408,"\int (e+f x) \sin \left(a+\frac{b}{(c+d x)^2}\right) \, dx","Integrate[(e + f*x)*Sin[a + b/(c + d*x)^2],x]","\frac{c^2 (-f) \sin \left(a+\frac{b}{(c+d x)^2}\right)-b f \cos (a) \text{Ci}\left(\frac{b}{(c+d x)^2}\right)+2 d^2 e x \sin \left(a+\frac{b}{(c+d x)^2}\right)+d^2 f x^2 \sin \left(a+\frac{b}{(c+d x)^2}\right)-2 \sqrt{2 \pi } \sqrt{b} \cos (a) (d e-c f) C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{c+d x}\right)+2 \sqrt{2 \pi } \sqrt{b} d e \sin (a) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{c+d x}\right)+2 c d e \sin \left(a+\frac{b}{(c+d x)^2}\right)-2 \sqrt{2 \pi } \sqrt{b} c f \sin (a) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{c+d x}\right)+b f \sin (a) \text{Si}\left(\frac{b}{(c+d x)^2}\right)}{2 d^2}","-\frac{b f \cos (a) \text{Ci}\left(\frac{b}{(c+d x)^2}\right)}{2 d^2}-\frac{\sqrt{2 \pi } \sqrt{b} \cos (a) (d e-c f) C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{c+d x}\right)}{d^2}+\frac{\sqrt{2 \pi } \sqrt{b} \sin (a) (d e-c f) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{c+d x}\right)}{d^2}+\frac{(c+d x) (d e-c f) \sin \left(a+\frac{b}{(c+d x)^2}\right)}{d^2}+\frac{b f \sin (a) \text{Si}\left(\frac{b}{(c+d x)^2}\right)}{2 d^2}+\frac{f (c+d x)^2 \sin \left(a+\frac{b}{(c+d x)^2}\right)}{2 d^2}",1,"(-(b*f*Cos[a]*CosIntegral[b/(c + d*x)^2]) - 2*Sqrt[b]*(d*e - c*f)*Sqrt[2*Pi]*Cos[a]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)] + 2*Sqrt[b]*d*e*Sqrt[2*Pi]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)]*Sin[a] - 2*Sqrt[b]*c*f*Sqrt[2*Pi]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)]*Sin[a] + 2*c*d*e*Sin[a + b/(c + d*x)^2] - c^2*f*Sin[a + b/(c + d*x)^2] + 2*d^2*e*x*Sin[a + b/(c + d*x)^2] + d^2*f*x^2*Sin[a + b/(c + d*x)^2] + b*f*Sin[a]*SinIntegral[b/(c + d*x)^2])/(2*d^2)","A",1
179,1,100,105,0.1746952,"\int \sin \left(a+\frac{b}{(c+d x)^2}\right) \, dx","Integrate[Sin[a + b/(c + d*x)^2],x]","\frac{\sqrt{2 \pi } \left(-\sqrt{b}\right) \cos (a) C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{c+d x}\right)+\sqrt{2 \pi } \sqrt{b} \sin (a) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{c+d x}\right)+(c+d x) \sin \left(a+\frac{b}{(c+d x)^2}\right)}{d}","-\frac{\sqrt{2 \pi } \sqrt{b} \cos (a) C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{c+d x}\right)}{d}+\frac{\sqrt{2 \pi } \sqrt{b} \sin (a) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{c+d x}\right)}{d}+\frac{(c+d x) \sin \left(a+\frac{b}{(c+d x)^2}\right)}{d}",1,"(-(Sqrt[b]*Sqrt[2*Pi]*Cos[a]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)]) + Sqrt[b]*Sqrt[2*Pi]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)]*Sin[a] + (c + d*x)*Sin[a + b/(c + d*x)^2])/d","A",1
180,0,0,23,5.1249854,"\int \frac{\sin \left(a+\frac{b}{(c+d x)^2}\right)}{e+f x} \, dx","Integrate[Sin[a + b/(c + d*x)^2]/(e + f*x),x]","\int \frac{\sin \left(a+\frac{b}{(c+d x)^2}\right)}{e+f x} \, dx","\text{Int}\left(\frac{\sin \left(a+\frac{b}{(c+d x)^2}\right)}{e+f x},x\right)",0,"Integrate[Sin[a + b/(c + d*x)^2]/(e + f*x), x]","A",-1
181,0,0,23,25.2774872,"\int \frac{\sin \left(a+\frac{b}{(c+d x)^2}\right)}{(e+f x)^2} \, dx","Integrate[Sin[a + b/(c + d*x)^2]/(e + f*x)^2,x]","\int \frac{\sin \left(a+\frac{b}{(c+d x)^2}\right)}{(e+f x)^2} \, dx","\text{Int}\left(\frac{\sin \left(a+\frac{b}{(c+d x)^2}\right)}{(e+f x)^2},x\right)",0,"Integrate[Sin[a + b/(c + d*x)^2]/(e + f*x)^2, x]","A",-1
182,1,405,330,2.6451661,"\int (e+f x)^2 \sin \left(a+\frac{b}{(c+d x)^3}\right) \, dx","Integrate[(e + f*x)^2*Sin[a + b/(c + d*x)^3],x]","\frac{\frac{3 b f (d e-c f) \left((\cos (a)-i \sin (a)) \sqrt[3]{-\frac{i b}{(c+d x)^3}} \Gamma \left(\frac{1}{3},\frac{i b}{(c+d x)^3}\right)+(\cos (a)+i \sin (a)) \sqrt[3]{\frac{i b}{(c+d x)^3}} \Gamma \left(\frac{1}{3},-\frac{i b}{(c+d x)^3}\right)\right)}{2 (c+d x) \sqrt[3]{\frac{b^2}{(c+d x)^6}}}+\frac{3 b (d e-c f)^2 \left((\cos (a)-i \sin (a)) \left(-\frac{i b}{(c+d x)^3}\right)^{2/3} \Gamma \left(\frac{2}{3},\frac{i b}{(c+d x)^3}\right)+(\cos (a)+i \sin (a)) \left(\frac{i b}{(c+d x)^3}\right)^{2/3} \Gamma \left(\frac{2}{3},-\frac{i b}{(c+d x)^3}\right)\right)}{2 (c+d x)^2 \left(\frac{b^2}{(c+d x)^6}\right)^{2/3}}+\sin (a) (c+d x) \cos \left(\frac{b}{(c+d x)^3}\right) \left(c^2 f^2-c d f (3 e+f x)+d^2 \left(3 e^2+3 e f x+f^2 x^2\right)\right)+\cos (a) (c+d x) \sin \left(\frac{b}{(c+d x)^3}\right) \left(c^2 f^2-c d f (3 e+f x)+d^2 \left(3 e^2+3 e f x+f^2 x^2\right)\right)-b f^2 \left(\cos (a) \text{Ci}\left(\frac{b}{(c+d x)^3}\right)-\sin (a) \text{Si}\left(\frac{b}{(c+d x)^3}\right)\right)}{3 d^3}","-\frac{b f^2 \cos (a) \text{Ci}\left(\frac{b}{(c+d x)^3}\right)}{3 d^3}-\frac{i e^{i a} f (c+d x)^2 \left(-\frac{i b}{(c+d x)^3}\right)^{2/3} (d e-c f) \Gamma \left(-\frac{2}{3},-\frac{i b}{(c+d x)^3}\right)}{3 d^3}+\frac{i e^{-i a} f (c+d x)^2 \left(\frac{i b}{(c+d x)^3}\right)^{2/3} (d e-c f) \Gamma \left(-\frac{2}{3},\frac{i b}{(c+d x)^3}\right)}{3 d^3}-\frac{i e^{i a} (c+d x) \sqrt[3]{-\frac{i b}{(c+d x)^3}} (d e-c f)^2 \Gamma \left(-\frac{1}{3},-\frac{i b}{(c+d x)^3}\right)}{6 d^3}+\frac{i e^{-i a} (c+d x) \sqrt[3]{\frac{i b}{(c+d x)^3}} (d e-c f)^2 \Gamma \left(-\frac{1}{3},\frac{i b}{(c+d x)^3}\right)}{6 d^3}+\frac{b f^2 \sin (a) \text{Si}\left(\frac{b}{(c+d x)^3}\right)}{3 d^3}+\frac{f^2 (c+d x)^3 \sin \left(a+\frac{b}{(c+d x)^3}\right)}{3 d^3}",1,"((3*b*f*(d*e - c*f)*((((-I)*b)/(c + d*x)^3)^(1/3)*Gamma[1/3, (I*b)/(c + d*x)^3]*(Cos[a] - I*Sin[a]) + ((I*b)/(c + d*x)^3)^(1/3)*Gamma[1/3, ((-I)*b)/(c + d*x)^3]*(Cos[a] + I*Sin[a])))/(2*(b^2/(c + d*x)^6)^(1/3)*(c + d*x)) + (3*b*(d*e - c*f)^2*((((-I)*b)/(c + d*x)^3)^(2/3)*Gamma[2/3, (I*b)/(c + d*x)^3]*(Cos[a] - I*Sin[a]) + ((I*b)/(c + d*x)^3)^(2/3)*Gamma[2/3, ((-I)*b)/(c + d*x)^3]*(Cos[a] + I*Sin[a])))/(2*(b^2/(c + d*x)^6)^(2/3)*(c + d*x)^2) + (c + d*x)*(c^2*f^2 - c*d*f*(3*e + f*x) + d^2*(3*e^2 + 3*e*f*x + f^2*x^2))*Cos[b/(c + d*x)^3]*Sin[a] + (c + d*x)*(c^2*f^2 - c*d*f*(3*e + f*x) + d^2*(3*e^2 + 3*e*f*x + f^2*x^2))*Cos[a]*Sin[b/(c + d*x)^3] - b*f^2*(Cos[a]*CosIntegral[b/(c + d*x)^3] - Sin[a]*SinIntegral[b/(c + d*x)^3]))/(3*d^3)","A",0
183,1,700,235,2.3498348,"\int (e+f x) \sin \left(a+\frac{b}{(c+d x)^3}\right) \, dx","Integrate[(e + f*x)*Sin[a + b/(c + d*x)^3],x]","\frac{f \sin (a) (d x-c) (c+d x) \cos \left(\frac{b}{(c+d x)^3}\right)}{2 d^2}+\frac{f \cos (a) (d x-c) (c+d x) \sin \left(\frac{b}{(c+d x)^3}\right)}{2 d^2}+\frac{3 b f \left(\frac{1}{2} \cos (a) \left(\frac{\Gamma \left(\frac{1}{3},-\frac{i b}{(c+d x)^3}\right)}{3 (c+d x) \sqrt[3]{-\frac{i b}{(c+d x)^3}}}+\frac{\Gamma \left(\frac{1}{3},\frac{i b}{(c+d x)^3}\right)}{3 (c+d x) \sqrt[3]{\frac{i b}{(c+d x)^3}}}\right)+\frac{1}{2} i \sin (a) \left(\frac{\Gamma \left(\frac{1}{3},-\frac{i b}{(c+d x)^3}\right)}{3 (c+d x) \sqrt[3]{-\frac{i b}{(c+d x)^3}}}-\frac{\Gamma \left(\frac{1}{3},\frac{i b}{(c+d x)^3}\right)}{3 (c+d x) \sqrt[3]{\frac{i b}{(c+d x)^3}}}\right)\right)}{2 d^2}-\frac{3 b c f \left(\frac{1}{2} \cos (a) \left(\frac{\Gamma \left(\frac{2}{3},-\frac{i b}{(c+d x)^3}\right)}{3 (c+d x)^2 \left(-\frac{i b}{(c+d x)^3}\right)^{2/3}}+\frac{\Gamma \left(\frac{2}{3},\frac{i b}{(c+d x)^3}\right)}{3 (c+d x)^2 \left(\frac{i b}{(c+d x)^3}\right)^{2/3}}\right)+\frac{1}{2} i \sin (a) \left(\frac{\Gamma \left(\frac{2}{3},-\frac{i b}{(c+d x)^3}\right)}{3 (c+d x)^2 \left(-\frac{i b}{(c+d x)^3}\right)^{2/3}}-\frac{\Gamma \left(\frac{2}{3},\frac{i b}{(c+d x)^3}\right)}{3 (c+d x)^2 \left(\frac{i b}{(c+d x)^3}\right)^{2/3}}\right)\right)}{d^2}+\frac{e \sin (a) (c+d x) \cos \left(\frac{b}{(c+d x)^3}\right)}{d}+\frac{e \cos (a) (c+d x) \sin \left(\frac{b}{(c+d x)^3}\right)}{d}+\frac{3 b e \left(\frac{1}{2} \cos (a) \left(\frac{\Gamma \left(\frac{2}{3},-\frac{i b}{(c+d x)^3}\right)}{3 (c+d x)^2 \left(-\frac{i b}{(c+d x)^3}\right)^{2/3}}+\frac{\Gamma \left(\frac{2}{3},\frac{i b}{(c+d x)^3}\right)}{3 (c+d x)^2 \left(\frac{i b}{(c+d x)^3}\right)^{2/3}}\right)+\frac{1}{2} i \sin (a) \left(\frac{\Gamma \left(\frac{2}{3},-\frac{i b}{(c+d x)^3}\right)}{3 (c+d x)^2 \left(-\frac{i b}{(c+d x)^3}\right)^{2/3}}-\frac{\Gamma \left(\frac{2}{3},\frac{i b}{(c+d x)^3}\right)}{3 (c+d x)^2 \left(\frac{i b}{(c+d x)^3}\right)^{2/3}}\right)\right)}{d}","-\frac{i e^{i a} (c+d x) \sqrt[3]{-\frac{i b}{(c+d x)^3}} (d e-c f) \Gamma \left(-\frac{1}{3},-\frac{i b}{(c+d x)^3}\right)}{6 d^2}+\frac{i e^{-i a} (c+d x) \sqrt[3]{\frac{i b}{(c+d x)^3}} (d e-c f) \Gamma \left(-\frac{1}{3},\frac{i b}{(c+d x)^3}\right)}{6 d^2}-\frac{i e^{i a} f (c+d x)^2 \left(-\frac{i b}{(c+d x)^3}\right)^{2/3} \Gamma \left(-\frac{2}{3},-\frac{i b}{(c+d x)^3}\right)}{6 d^2}+\frac{i e^{-i a} f (c+d x)^2 \left(\frac{i b}{(c+d x)^3}\right)^{2/3} \Gamma \left(-\frac{2}{3},\frac{i b}{(c+d x)^3}\right)}{6 d^2}",1,"(e*(c + d*x)*Cos[b/(c + d*x)^3]*Sin[a])/d + (f*(-c + d*x)*(c + d*x)*Cos[b/(c + d*x)^3]*Sin[a])/(2*d^2) + (3*b*f*((Cos[a]*(Gamma[1/3, ((-I)*b)/(c + d*x)^3]/(3*(((-I)*b)/(c + d*x)^3)^(1/3)*(c + d*x)) + Gamma[1/3, (I*b)/(c + d*x)^3]/(3*((I*b)/(c + d*x)^3)^(1/3)*(c + d*x))))/2 + (I/2)*(Gamma[1/3, ((-I)*b)/(c + d*x)^3]/(3*(((-I)*b)/(c + d*x)^3)^(1/3)*(c + d*x)) - Gamma[1/3, (I*b)/(c + d*x)^3]/(3*((I*b)/(c + d*x)^3)^(1/3)*(c + d*x)))*Sin[a]))/(2*d^2) + (3*b*e*((Cos[a]*(Gamma[2/3, ((-I)*b)/(c + d*x)^3]/(3*(((-I)*b)/(c + d*x)^3)^(2/3)*(c + d*x)^2) + Gamma[2/3, (I*b)/(c + d*x)^3]/(3*((I*b)/(c + d*x)^3)^(2/3)*(c + d*x)^2)))/2 + (I/2)*(Gamma[2/3, ((-I)*b)/(c + d*x)^3]/(3*(((-I)*b)/(c + d*x)^3)^(2/3)*(c + d*x)^2) - Gamma[2/3, (I*b)/(c + d*x)^3]/(3*((I*b)/(c + d*x)^3)^(2/3)*(c + d*x)^2))*Sin[a]))/d - (3*b*c*f*((Cos[a]*(Gamma[2/3, ((-I)*b)/(c + d*x)^3]/(3*(((-I)*b)/(c + d*x)^3)^(2/3)*(c + d*x)^2) + Gamma[2/3, (I*b)/(c + d*x)^3]/(3*((I*b)/(c + d*x)^3)^(2/3)*(c + d*x)^2)))/2 + (I/2)*(Gamma[2/3, ((-I)*b)/(c + d*x)^3]/(3*(((-I)*b)/(c + d*x)^3)^(2/3)*(c + d*x)^2) - Gamma[2/3, (I*b)/(c + d*x)^3]/(3*((I*b)/(c + d*x)^3)^(2/3)*(c + d*x)^2))*Sin[a]))/d^2 + (e*(c + d*x)*Cos[a]*Sin[b/(c + d*x)^3])/d + (f*(-c + d*x)*(c + d*x)*Cos[a]*Sin[b/(c + d*x)^3])/(2*d^2)","B",1
184,1,203,107,0.5071572,"\int \sin \left(a+\frac{b}{(c+d x)^3}\right) \, dx","Integrate[Sin[a + b/(c + d*x)^3],x]","\frac{2 \sin (a) (c+d x)^3 \cos \left(\frac{b}{(c+d x)^3}\right)+2 \cos (a) (c+d x)^3 \sin \left(\frac{b}{(c+d x)^3}\right)+b \cos (a) \left(\frac{\Gamma \left(\frac{2}{3},-\frac{i b}{(c+d x)^3}\right)}{\left(-\frac{i b}{(c+d x)^3}\right)^{2/3}}+\frac{\Gamma \left(\frac{2}{3},\frac{i b}{(c+d x)^3}\right)}{\left(\frac{i b}{(c+d x)^3}\right)^{2/3}}\right)+i b \sin (a) \left(\frac{\Gamma \left(\frac{2}{3},-\frac{i b}{(c+d x)^3}\right)}{\left(-\frac{i b}{(c+d x)^3}\right)^{2/3}}-\frac{\Gamma \left(\frac{2}{3},\frac{i b}{(c+d x)^3}\right)}{\left(\frac{i b}{(c+d x)^3}\right)^{2/3}}\right)}{2 d (c+d x)^2}","\frac{i e^{-i a} (c+d x) \sqrt[3]{\frac{i b}{(c+d x)^3}} \Gamma \left(-\frac{1}{3},\frac{i b}{(c+d x)^3}\right)}{6 d}-\frac{i e^{i a} (c+d x) \sqrt[3]{-\frac{i b}{(c+d x)^3}} \Gamma \left(-\frac{1}{3},-\frac{i b}{(c+d x)^3}\right)}{6 d}",1,"(b*Cos[a]*(Gamma[2/3, ((-I)*b)/(c + d*x)^3]/(((-I)*b)/(c + d*x)^3)^(2/3) + Gamma[2/3, (I*b)/(c + d*x)^3]/((I*b)/(c + d*x)^3)^(2/3)) + 2*(c + d*x)^3*Cos[b/(c + d*x)^3]*Sin[a] + I*b*(Gamma[2/3, ((-I)*b)/(c + d*x)^3]/(((-I)*b)/(c + d*x)^3)^(2/3) - Gamma[2/3, (I*b)/(c + d*x)^3]/((I*b)/(c + d*x)^3)^(2/3))*Sin[a] + 2*(c + d*x)^3*Cos[a]*Sin[b/(c + d*x)^3])/(2*d*(c + d*x)^2)","A",1
185,0,0,23,5.1508906,"\int \frac{\sin \left(a+\frac{b}{(c+d x)^3}\right)}{e+f x} \, dx","Integrate[Sin[a + b/(c + d*x)^3]/(e + f*x),x]","\int \frac{\sin \left(a+\frac{b}{(c+d x)^3}\right)}{e+f x} \, dx","\text{Int}\left(\frac{\sin \left(a+\frac{b}{(c+d x)^3}\right)}{e+f x},x\right)",0,"Integrate[Sin[a + b/(c + d*x)^3]/(e + f*x), x]","A",-1
186,0,0,23,29.6712186,"\int \frac{\sin \left(a+\frac{b}{(c+d x)^3}\right)}{(e+f x)^2} \, dx","Integrate[Sin[a + b/(c + d*x)^3]/(e + f*x)^2,x]","\int \frac{\sin \left(a+\frac{b}{(c+d x)^3}\right)}{(e+f x)^2} \, dx","\text{Int}\left(\frac{\sin \left(a+\frac{b}{(c+d x)^3}\right)}{(e+f x)^2},x\right)",0,"Integrate[Sin[a + b/(c + d*x)^3]/(e + f*x)^2, x]","A",-1
187,1,138,410,1.8720359,"\int (e+f x)^2 \sin \left(a+b \sqrt{c+d x}\right) \, dx","Integrate[(e + f*x)^2*Sin[a + b*Sqrt[c + d*x]],x]","\frac{2 \sin \left(a+b \sqrt{c+d x}\right) \left(b^4 d (e+f x) (4 c f+d (e+5 f x))-12 b^2 f (4 c f+d (e+5 f x))+120 f^2\right)-2 b \sqrt{c+d x} \cos \left(a+b \sqrt{c+d x}\right) \left(b^4 d^2 (e+f x)^2-4 b^2 f (2 c f+3 d e+5 d f x)+120 f^2\right)}{b^6 d^3}","\frac{240 f^2 \sin \left(a+b \sqrt{c+d x}\right)}{b^6 d^3}-\frac{240 f^2 \sqrt{c+d x} \cos \left(a+b \sqrt{c+d x}\right)}{b^5 d^3}-\frac{24 f (d e-c f) \sin \left(a+b \sqrt{c+d x}\right)}{b^4 d^3}-\frac{120 f^2 (c+d x) \sin \left(a+b \sqrt{c+d x}\right)}{b^4 d^3}+\frac{24 f \sqrt{c+d x} (d e-c f) \cos \left(a+b \sqrt{c+d x}\right)}{b^3 d^3}+\frac{40 f^2 (c+d x)^{3/2} \cos \left(a+b \sqrt{c+d x}\right)}{b^3 d^3}+\frac{12 f (c+d x) (d e-c f) \sin \left(a+b \sqrt{c+d x}\right)}{b^2 d^3}+\frac{2 (d e-c f)^2 \sin \left(a+b \sqrt{c+d x}\right)}{b^2 d^3}+\frac{10 f^2 (c+d x)^2 \sin \left(a+b \sqrt{c+d x}\right)}{b^2 d^3}-\frac{4 f (c+d x)^{3/2} (d e-c f) \cos \left(a+b \sqrt{c+d x}\right)}{b d^3}-\frac{2 \sqrt{c+d x} (d e-c f)^2 \cos \left(a+b \sqrt{c+d x}\right)}{b d^3}-\frac{2 f^2 (c+d x)^{5/2} \cos \left(a+b \sqrt{c+d x}\right)}{b d^3}",1,"(-2*b*Sqrt[c + d*x]*(120*f^2 + b^4*d^2*(e + f*x)^2 - 4*b^2*f*(3*d*e + 2*c*f + 5*d*f*x))*Cos[a + b*Sqrt[c + d*x]] + 2*(120*f^2 - 12*b^2*f*(4*c*f + d*(e + 5*f*x)) + b^4*d*(e + f*x)*(4*c*f + d*(e + 5*f*x)))*Sin[a + b*Sqrt[c + d*x]])/(b^6*d^3)","A",1
188,1,85,185,0.4477624,"\int (e+f x) \sin \left(a+b \sqrt{c+d x}\right) \, dx","Integrate[(e + f*x)*Sin[a + b*Sqrt[c + d*x]],x]","\frac{2 \sin \left(a+b \sqrt{c+d x}\right) \left(b^2 (2 c f+d (e+3 f x))-6 f\right)-2 b \sqrt{c+d x} \left(b^2 d (e+f x)-6 f\right) \cos \left(a+b \sqrt{c+d x}\right)}{b^4 d^2}","-\frac{12 f \sin \left(a+b \sqrt{c+d x}\right)}{b^4 d^2}+\frac{12 f \sqrt{c+d x} \cos \left(a+b \sqrt{c+d x}\right)}{b^3 d^2}+\frac{2 (d e-c f) \sin \left(a+b \sqrt{c+d x}\right)}{b^2 d^2}+\frac{6 f (c+d x) \sin \left(a+b \sqrt{c+d x}\right)}{b^2 d^2}-\frac{2 \sqrt{c+d x} (d e-c f) \cos \left(a+b \sqrt{c+d x}\right)}{b d^2}-\frac{2 f (c+d x)^{3/2} \cos \left(a+b \sqrt{c+d x}\right)}{b d^2}",1,"(-2*b*Sqrt[c + d*x]*(-6*f + b^2*d*(e + f*x))*Cos[a + b*Sqrt[c + d*x]] + 2*(-6*f + b^2*(2*c*f + d*(e + 3*f*x)))*Sin[a + b*Sqrt[c + d*x]])/(b^4*d^2)","A",1
189,1,50,54,0.0772315,"\int \sin \left(a+b \sqrt{c+d x}\right) \, dx","Integrate[Sin[a + b*Sqrt[c + d*x]],x]","\frac{2 \sin \left(a+b \sqrt{c+d x}\right)-2 b \sqrt{c+d x} \cos \left(a+b \sqrt{c+d x}\right)}{b^2 d}","\frac{2 \sin \left(a+b \sqrt{c+d x}\right)}{b^2 d}-\frac{2 \sqrt{c+d x} \cos \left(a+b \sqrt{c+d x}\right)}{b d}",1,"(-2*b*Sqrt[c + d*x]*Cos[a + b*Sqrt[c + d*x]] + 2*Sin[a + b*Sqrt[c + d*x]])/(b^2*d)","A",1
190,1,238,238,1.5511281,"\int \frac{\sin \left(a+b \sqrt{c+d x}\right)}{e+f x} \, dx","Integrate[Sin[a + b*Sqrt[c + d*x]]/(e + f*x),x]","\frac{i e^{-i \left(a+\frac{b \sqrt{c f-d e}}{\sqrt{f}}\right)} \left(-e^{2 i \left(a+\frac{b \sqrt{c f-d e}}{\sqrt{f}}\right)} \text{Ei}\left(i b \left(\sqrt{c+d x}-\frac{\sqrt{c f-d e}}{\sqrt{f}}\right)\right)-e^{2 i a} \text{Ei}\left(i b \left(\frac{\sqrt{c f-d e}}{\sqrt{f}}+\sqrt{c+d x}\right)\right)+\text{Ei}\left(-i b \left(\sqrt{c+d x}-\frac{\sqrt{c f-d e}}{\sqrt{f}}\right)\right)+e^{\frac{2 i b \sqrt{c f-d e}}{\sqrt{f}}} \text{Ei}\left(-i b \left(\frac{\sqrt{c f-d e}}{\sqrt{f}}+\sqrt{c+d x}\right)\right)\right)}{2 f}","\frac{\sin \left(a-\frac{b \sqrt{c f-d e}}{\sqrt{f}}\right) \text{Ci}\left(\frac{\sqrt{c f-d e} b}{\sqrt{f}}+\sqrt{c+d x} b\right)}{f}+\frac{\sin \left(a+\frac{b \sqrt{c f-d e}}{\sqrt{f}}\right) \text{Ci}\left(\frac{b \sqrt{c f-d e}}{\sqrt{f}}-b \sqrt{c+d x}\right)}{f}-\frac{\cos \left(a+\frac{b \sqrt{c f-d e}}{\sqrt{f}}\right) \text{Si}\left(\frac{b \sqrt{c f-d e}}{\sqrt{f}}-b \sqrt{c+d x}\right)}{f}+\frac{\cos \left(a-\frac{b \sqrt{c f-d e}}{\sqrt{f}}\right) \text{Si}\left(\frac{\sqrt{c f-d e} b}{\sqrt{f}}+\sqrt{c+d x} b\right)}{f}",1,"((I/2)*(ExpIntegralEi[(-I)*b*(-(Sqrt[-(d*e) + c*f]/Sqrt[f]) + Sqrt[c + d*x])] - E^((2*I)*(a + (b*Sqrt[-(d*e) + c*f])/Sqrt[f]))*ExpIntegralEi[I*b*(-(Sqrt[-(d*e) + c*f]/Sqrt[f]) + Sqrt[c + d*x])] + E^(((2*I)*b*Sqrt[-(d*e) + c*f])/Sqrt[f])*ExpIntegralEi[(-I)*b*(Sqrt[-(d*e) + c*f]/Sqrt[f] + Sqrt[c + d*x])] - E^((2*I)*a)*ExpIntegralEi[I*b*(Sqrt[-(d*e) + c*f]/Sqrt[f] + Sqrt[c + d*x])]))/(E^(I*(a + (b*Sqrt[-(d*e) + c*f])/Sqrt[f]))*f)","C",1
191,1,397,339,3.6066186,"\int \frac{\sin \left(a+b \sqrt{c+d x}\right)}{(e+f x)^2} \, dx","Integrate[Sin[a + b*Sqrt[c + d*x]]/(e + f*x)^2,x]","\frac{i e^{-i a} d \left(e^{2 i a} \left(-\frac{i b e^{\frac{i b \sqrt{c f-d e}}{\sqrt{f}}} \text{Ei}\left(i b \left(\sqrt{c+d x}-\frac{\sqrt{c f-d e}}{\sqrt{f}}\right)\right)}{\sqrt{c f-d e}}+\frac{i b e^{-\frac{i b \sqrt{c f-d e}}{\sqrt{f}}} \text{Ei}\left(i b \left(\frac{\sqrt{c f-d e}}{\sqrt{f}}+\sqrt{c+d x}\right)\right)}{\sqrt{c f-d e}}+\frac{2 \sqrt{f} e^{i b \sqrt{c+d x}}}{d e+d f x}\right)-\frac{i b e^{-\frac{i b \sqrt{c f-d e}}{\sqrt{f}}} \text{Ei}\left(-i b \left(\sqrt{c+d x}-\frac{\sqrt{c f-d e}}{\sqrt{f}}\right)\right)}{\sqrt{c f-d e}}+\frac{i b e^{\frac{i b \sqrt{c f-d e}}{\sqrt{f}}} \text{Ei}\left(-i b \left(\frac{\sqrt{c f-d e}}{\sqrt{f}}+\sqrt{c+d x}\right)\right)}{\sqrt{c f-d e}}-\frac{2 \sqrt{f} e^{-i b \sqrt{c+d x}}}{d e+d f x}\right)}{4 f^{3/2}}","\frac{b d \cos \left(a+\frac{b \sqrt{c f-d e}}{\sqrt{f}}\right) \text{Ci}\left(\frac{b \sqrt{c f-d e}}{\sqrt{f}}-b \sqrt{c+d x}\right)}{2 f^{3/2} \sqrt{c f-d e}}-\frac{b d \cos \left(a-\frac{b \sqrt{c f-d e}}{\sqrt{f}}\right) \text{Ci}\left(\frac{\sqrt{c f-d e} b}{\sqrt{f}}+\sqrt{c+d x} b\right)}{2 f^{3/2} \sqrt{c f-d e}}+\frac{b d \sin \left(a+\frac{b \sqrt{c f-d e}}{\sqrt{f}}\right) \text{Si}\left(\frac{b \sqrt{c f-d e}}{\sqrt{f}}-b \sqrt{c+d x}\right)}{2 f^{3/2} \sqrt{c f-d e}}+\frac{b d \sin \left(a-\frac{b \sqrt{c f-d e}}{\sqrt{f}}\right) \text{Si}\left(\frac{\sqrt{c f-d e} b}{\sqrt{f}}+\sqrt{c+d x} b\right)}{2 f^{3/2} \sqrt{c f-d e}}-\frac{\sin \left(a+b \sqrt{c+d x}\right)}{f (e+f x)}",1,"((I/4)*d*((-2*Sqrt[f])/(E^(I*b*Sqrt[c + d*x])*(d*e + d*f*x)) - (I*b*ExpIntegralEi[(-I)*b*(-(Sqrt[-(d*e) + c*f]/Sqrt[f]) + Sqrt[c + d*x])])/(E^((I*b*Sqrt[-(d*e) + c*f])/Sqrt[f])*Sqrt[-(d*e) + c*f]) + (I*b*E^((I*b*Sqrt[-(d*e) + c*f])/Sqrt[f])*ExpIntegralEi[(-I)*b*(Sqrt[-(d*e) + c*f]/Sqrt[f] + Sqrt[c + d*x])])/Sqrt[-(d*e) + c*f] + E^((2*I)*a)*((2*E^(I*b*Sqrt[c + d*x])*Sqrt[f])/(d*e + d*f*x) - (I*b*E^((I*b*Sqrt[-(d*e) + c*f])/Sqrt[f])*ExpIntegralEi[I*b*(-(Sqrt[-(d*e) + c*f]/Sqrt[f]) + Sqrt[c + d*x])])/Sqrt[-(d*e) + c*f] + (I*b*ExpIntegralEi[I*b*(Sqrt[-(d*e) + c*f]/Sqrt[f] + Sqrt[c + d*x])])/(E^((I*b*Sqrt[-(d*e) + c*f])/Sqrt[f])*Sqrt[-(d*e) + c*f]))))/(E^(I*a)*f^(3/2))","C",1
192,1,419,382,3.2491087,"\int (e+f x)^2 \sin \left(a+b (c+d x)^{3/2}\right) \, dx","Integrate[(e + f*x)^2*Sin[a + b*(c + d*x)^(3/2)],x]","-\frac{i \left((\cos (a)+i \sin (a)) \left(\frac{i f^2 \sin \left(b (c+d x)^{3/2}\right)}{b^2}+\frac{f^2 \cos \left(b (c+d x)^{3/2}\right)}{b^2}-\frac{2 f (c+d x)^2 (d e-c f) \Gamma \left(\frac{4}{3},-i b (c+d x)^{3/2}\right)}{\left(-i b (c+d x)^{3/2}\right)^{4/3}}-\frac{(c+d x) (d e-c f)^2 \Gamma \left(\frac{2}{3},-i b (c+d x)^{3/2}\right)}{\left(-i b (c+d x)^{3/2}\right)^{2/3}}+\frac{f^2 (c+d x)^{3/2} \left(\sin \left(b (c+d x)^{3/2}\right)-i \cos \left(b (c+d x)^{3/2}\right)\right)}{b}\right)-(\cos (a)-i \sin (a)) \left(-\frac{i f^2 \sin \left(b (c+d x)^{3/2}\right)}{b^2}+\frac{f^2 \cos \left(b (c+d x)^{3/2}\right)}{b^2}-\frac{2 f (c+d x)^2 (d e-c f) \Gamma \left(\frac{4}{3},i b (c+d x)^{3/2}\right)}{\left(i b (c+d x)^{3/2}\right)^{4/3}}-\frac{(c+d x) (d e-c f)^2 \Gamma \left(\frac{2}{3},i b (c+d x)^{3/2}\right)}{\left(i b (c+d x)^{3/2}\right)^{2/3}}+\frac{f^2 (c+d x)^{3/2} \left(\sin \left(b (c+d x)^{3/2}\right)+i \cos \left(b (c+d x)^{3/2}\right)\right)}{b}\right)\right)}{3 d^3}","\frac{2 f^2 \sin \left(a+b (c+d x)^{3/2}\right)}{3 b^2 d^3}-\frac{4 f \sqrt{c+d x} (d e-c f) \cos \left(a+b (c+d x)^{3/2}\right)}{3 b d^3}-\frac{2 e^{i a} f \sqrt{c+d x} (d e-c f) \Gamma \left(\frac{1}{3},-i b (c+d x)^{3/2}\right)}{9 b d^3 \sqrt[3]{-i b (c+d x)^{3/2}}}-\frac{2 e^{-i a} f \sqrt{c+d x} (d e-c f) \Gamma \left(\frac{1}{3},i b (c+d x)^{3/2}\right)}{9 b d^3 \sqrt[3]{i b (c+d x)^{3/2}}}+\frac{i e^{i a} (c+d x) (d e-c f)^2 \Gamma \left(\frac{2}{3},-i b (c+d x)^{3/2}\right)}{3 d^3 \left(-i b (c+d x)^{3/2}\right)^{2/3}}-\frac{i e^{-i a} (c+d x) (d e-c f)^2 \Gamma \left(\frac{2}{3},i b (c+d x)^{3/2}\right)}{3 d^3 \left(i b (c+d x)^{3/2}\right)^{2/3}}-\frac{2 f^2 (c+d x)^{3/2} \cos \left(a+b (c+d x)^{3/2}\right)}{3 b d^3}",1,"((-1/3*I)*((Cos[a] + I*Sin[a])*((f^2*Cos[b*(c + d*x)^(3/2)])/b^2 - ((d*e - c*f)^2*(c + d*x)*Gamma[2/3, (-I)*b*(c + d*x)^(3/2)])/((-I)*b*(c + d*x)^(3/2))^(2/3) - (2*f*(d*e - c*f)*(c + d*x)^2*Gamma[4/3, (-I)*b*(c + d*x)^(3/2)])/((-I)*b*(c + d*x)^(3/2))^(4/3) + (I*f^2*Sin[b*(c + d*x)^(3/2)])/b^2 + (f^2*(c + d*x)^(3/2)*((-I)*Cos[b*(c + d*x)^(3/2)] + Sin[b*(c + d*x)^(3/2)]))/b) - (Cos[a] - I*Sin[a])*((f^2*Cos[b*(c + d*x)^(3/2)])/b^2 - ((d*e - c*f)^2*(c + d*x)*Gamma[2/3, I*b*(c + d*x)^(3/2)])/(I*b*(c + d*x)^(3/2))^(2/3) - (2*f*(d*e - c*f)*(c + d*x)^2*Gamma[4/3, I*b*(c + d*x)^(3/2)])/(I*b*(c + d*x)^(3/2))^(4/3) - (I*f^2*Sin[b*(c + d*x)^(3/2)])/b^2 + (f^2*(c + d*x)^(3/2)*(I*Cos[b*(c + d*x)^(3/2)] + Sin[b*(c + d*x)^(3/2)]))/b)))/d^3","A",1
193,1,705,291,2.6319429,"\int (e+f x) \sin \left(a+b (c+d x)^{3/2}\right) \, dx","Integrate[(e + f*x)*Sin[a + b*(c + d*x)^(3/2)],x]","\frac{2 f \sin (a) \sqrt{c+d x} \sin \left(b (c+d x)^{3/2}\right)}{3 b d^2}-\frac{2 f \cos (a) \sqrt{c+d x} \cos \left(b (c+d x)^{3/2}\right)}{3 b d^2}+\frac{f \cos (a) \left(-\frac{2 \sqrt{c+d x} \Gamma \left(\frac{1}{3},-i b (c+d x)^{3/2}\right)}{3 \sqrt[3]{-i b (c+d x)^{3/2}}}-\frac{2 \sqrt{c+d x} \Gamma \left(\frac{1}{3},i b (c+d x)^{3/2}\right)}{3 \sqrt[3]{i b (c+d x)^{3/2}}}\right)}{6 b d^2}+\frac{i c f \cos (a) \left(\frac{2 (c+d x) \Gamma \left(\frac{2}{3},i b (c+d x)^{3/2}\right)}{3 \left(i b (c+d x)^{3/2}\right)^{2/3}}-\frac{2 (c+d x) \Gamma \left(\frac{2}{3},-i b (c+d x)^{3/2}\right)}{3 \left(-i b (c+d x)^{3/2}\right)^{2/3}}\right)}{2 d^2}+\frac{i f \sin (a) \left(\frac{2 \sqrt{c+d x} \Gamma \left(\frac{1}{3},i b (c+d x)^{3/2}\right)}{3 \sqrt[3]{i b (c+d x)^{3/2}}}-\frac{2 \sqrt{c+d x} \Gamma \left(\frac{1}{3},-i b (c+d x)^{3/2}\right)}{3 \sqrt[3]{-i b (c+d x)^{3/2}}}\right)}{6 b d^2}-\frac{c f \sin (a) \left(-\frac{2 (c+d x) \Gamma \left(\frac{2}{3},-i b (c+d x)^{3/2}\right)}{3 \left(-i b (c+d x)^{3/2}\right)^{2/3}}-\frac{2 (c+d x) \Gamma \left(\frac{2}{3},i b (c+d x)^{3/2}\right)}{3 \left(i b (c+d x)^{3/2}\right)^{2/3}}\right)}{2 d^2}-\frac{i e \cos (a) \left(\frac{2 (c+d x) \Gamma \left(\frac{2}{3},i b (c+d x)^{3/2}\right)}{3 \left(i b (c+d x)^{3/2}\right)^{2/3}}-\frac{2 (c+d x) \Gamma \left(\frac{2}{3},-i b (c+d x)^{3/2}\right)}{3 \left(-i b (c+d x)^{3/2}\right)^{2/3}}\right)}{2 d}+\frac{e \sin (a) \left(-\frac{2 (c+d x) \Gamma \left(\frac{2}{3},-i b (c+d x)^{3/2}\right)}{3 \left(-i b (c+d x)^{3/2}\right)^{2/3}}-\frac{2 (c+d x) \Gamma \left(\frac{2}{3},i b (c+d x)^{3/2}\right)}{3 \left(i b (c+d x)^{3/2}\right)^{2/3}}\right)}{2 d}","\frac{i e^{i a} (c+d x) (d e-c f) \Gamma \left(\frac{2}{3},-i b (c+d x)^{3/2}\right)}{3 d^2 \left(-i b (c+d x)^{3/2}\right)^{2/3}}-\frac{i e^{-i a} (c+d x) (d e-c f) \Gamma \left(\frac{2}{3},i b (c+d x)^{3/2}\right)}{3 d^2 \left(i b (c+d x)^{3/2}\right)^{2/3}}-\frac{2 f \sqrt{c+d x} \cos \left(a+b (c+d x)^{3/2}\right)}{3 b d^2}-\frac{e^{i a} f \sqrt{c+d x} \Gamma \left(\frac{1}{3},-i b (c+d x)^{3/2}\right)}{9 b d^2 \sqrt[3]{-i b (c+d x)^{3/2}}}-\frac{e^{-i a} f \sqrt{c+d x} \Gamma \left(\frac{1}{3},i b (c+d x)^{3/2}\right)}{9 b d^2 \sqrt[3]{i b (c+d x)^{3/2}}}",1,"(-2*f*Sqrt[c + d*x]*Cos[a]*Cos[b*(c + d*x)^(3/2)])/(3*b*d^2) + (f*Cos[a]*((-2*Sqrt[c + d*x]*Gamma[1/3, (-I)*b*(c + d*x)^(3/2)])/(3*((-I)*b*(c + d*x)^(3/2))^(1/3)) - (2*Sqrt[c + d*x]*Gamma[1/3, I*b*(c + d*x)^(3/2)])/(3*(I*b*(c + d*x)^(3/2))^(1/3))))/(6*b*d^2) - ((I/2)*e*Cos[a]*((-2*(c + d*x)*Gamma[2/3, (-I)*b*(c + d*x)^(3/2)])/(3*((-I)*b*(c + d*x)^(3/2))^(2/3)) + (2*(c + d*x)*Gamma[2/3, I*b*(c + d*x)^(3/2)])/(3*(I*b*(c + d*x)^(3/2))^(2/3))))/d + ((I/2)*c*f*Cos[a]*((-2*(c + d*x)*Gamma[2/3, (-I)*b*(c + d*x)^(3/2)])/(3*((-I)*b*(c + d*x)^(3/2))^(2/3)) + (2*(c + d*x)*Gamma[2/3, I*b*(c + d*x)^(3/2)])/(3*(I*b*(c + d*x)^(3/2))^(2/3))))/d^2 + ((I/6)*f*((-2*Sqrt[c + d*x]*Gamma[1/3, (-I)*b*(c + d*x)^(3/2)])/(3*((-I)*b*(c + d*x)^(3/2))^(1/3)) + (2*Sqrt[c + d*x]*Gamma[1/3, I*b*(c + d*x)^(3/2)])/(3*(I*b*(c + d*x)^(3/2))^(1/3)))*Sin[a])/(b*d^2) + (e*((-2*(c + d*x)*Gamma[2/3, (-I)*b*(c + d*x)^(3/2)])/(3*((-I)*b*(c + d*x)^(3/2))^(2/3)) - (2*(c + d*x)*Gamma[2/3, I*b*(c + d*x)^(3/2)])/(3*(I*b*(c + d*x)^(3/2))^(2/3)))*Sin[a])/(2*d) - (c*f*((-2*(c + d*x)*Gamma[2/3, (-I)*b*(c + d*x)^(3/2)])/(3*((-I)*b*(c + d*x)^(3/2))^(2/3)) - (2*(c + d*x)*Gamma[2/3, I*b*(c + d*x)^(3/2)])/(3*(I*b*(c + d*x)^(3/2))^(2/3)))*Sin[a])/(2*d^2) + (2*f*Sqrt[c + d*x]*Sin[a]*Sin[b*(c + d*x)^(3/2)])/(3*b*d^2)","B",1
194,1,123,115,0.1533755,"\int \sin \left(a+b (c+d x)^{3/2}\right) \, dx","Integrate[Sin[a + b*(c + d*x)^(3/2)],x]","\frac{i (c+d x) \left((\cos (a)+i \sin (a)) \left(i b (c+d x)^{3/2}\right)^{2/3} \Gamma \left(\frac{2}{3},-i b (c+d x)^{3/2}\right)-(\cos (a)-i \sin (a)) \left(-i b (c+d x)^{3/2}\right)^{2/3} \Gamma \left(\frac{2}{3},i b (c+d x)^{3/2}\right)\right)}{3 d \left(b^2 (c+d x)^3\right)^{2/3}}","\frac{i e^{i a} (c+d x) \Gamma \left(\frac{2}{3},-i b (c+d x)^{3/2}\right)}{3 d \left(-i b (c+d x)^{3/2}\right)^{2/3}}-\frac{i e^{-i a} (c+d x) \Gamma \left(\frac{2}{3},i b (c+d x)^{3/2}\right)}{3 d \left(i b (c+d x)^{3/2}\right)^{2/3}}",1,"((I/3)*(c + d*x)*(-(((-I)*b*(c + d*x)^(3/2))^(2/3)*Gamma[2/3, I*b*(c + d*x)^(3/2)]*(Cos[a] - I*Sin[a])) + (I*b*(c + d*x)^(3/2))^(2/3)*Gamma[2/3, (-I)*b*(c + d*x)^(3/2)]*(Cos[a] + I*Sin[a])))/(d*(b^2*(c + d*x)^3)^(2/3))","A",1
195,0,0,25,11.0839891,"\int \frac{\sin \left(a+b (c+d x)^{3/2}\right)}{e+f x} \, dx","Integrate[Sin[a + b*(c + d*x)^(3/2)]/(e + f*x),x]","\int \frac{\sin \left(a+b (c+d x)^{3/2}\right)}{e+f x} \, dx","\text{Int}\left(\frac{\sin \left(a+b (c+d x)^{3/2}\right)}{e+f x},x\right)",0,"Integrate[Sin[a + b*(c + d*x)^(3/2)]/(e + f*x), x]","A",-1
196,0,0,25,13.9214513,"\int \frac{\sin \left(a+b (c+d x)^{3/2}\right)}{(e+f x)^2} \, dx","Integrate[Sin[a + b*(c + d*x)^(3/2)]/(e + f*x)^2,x]","\int \frac{\sin \left(a+b (c+d x)^{3/2}\right)}{(e+f x)^2} \, dx","\text{Int}\left(\frac{\sin \left(a+b (c+d x)^{3/2}\right)}{(e+f x)^2},x\right)",0,"Integrate[Sin[a + b*(c + d*x)^(3/2)]/(e + f*x)^2, x]","A",-1
197,1,557,611,2.2972804,"\int (e+f x)^2 \sin \left(a+\frac{b}{\sqrt{c+d x}}\right) \, dx","Integrate[(e + f*x)^2*Sin[a + b/Sqrt[c + d*x]],x]","\frac{i e^{-i a} \left(-e^{2 i a} b^2 \left(-60 d e f \left(b^2+12 c\right)+f^2 \left(b^4+60 b^2 c+360 c^2\right)+360 d^2 e^2\right) \text{Ei}\left(\frac{i b}{\sqrt{c+d x}}\right)-\sqrt{c+d x} e^{i \left(2 a+\frac{b}{\sqrt{c+d x}}\right)} \left(i b^5 f^2+b^4 f^2 \sqrt{c+d x}-2 i b^3 f (-29 c f+30 d e+d f x)-6 b^2 f \sqrt{c+d x} (-9 c f+10 d e+d f x)+24 i b \left(11 c^2 f^2-c d f (25 e+3 f x)+d^2 \left(15 e^2+5 e f x+f^2 x^2\right)\right)+120 \sqrt{c+d x} \left(c^2 f^2-c d f (3 e+f x)+d^2 \left(3 e^2+3 e f x+f^2 x^2\right)\right)\right)+b^2 \left(-60 d e f \left(b^2+12 c\right)+f^2 \left(b^4+60 b^2 c+360 c^2\right)+360 d^2 e^2\right) \text{Ei}\left(-\frac{i b}{\sqrt{c+d x}}\right)+\sqrt{c+d x} e^{-\frac{i b}{\sqrt{c+d x}}} \left(-i b^5 f^2+b^4 f^2 \sqrt{c+d x}+2 i b^3 f (-29 c f+30 d e+d f x)-6 b^2 f \sqrt{c+d x} (-9 c f+10 d e+d f x)-24 i b \left(11 c^2 f^2-c d f (25 e+3 f x)+d^2 \left(15 e^2+5 e f x+f^2 x^2\right)\right)+120 \sqrt{c+d x} \left(c^2 f^2-c d f (3 e+f x)+d^2 \left(3 e^2+3 e f x+f^2 x^2\right)\right)\right)\right)}{720 d^3}","\frac{b^6 f^2 \sin (a) \text{Ci}\left(\frac{b}{\sqrt{c+d x}}\right)}{360 d^3}+\frac{b^6 f^2 \cos (a) \text{Si}\left(\frac{b}{\sqrt{c+d x}}\right)}{360 d^3}+\frac{b^5 f^2 \sqrt{c+d x} \cos \left(a+\frac{b}{\sqrt{c+d x}}\right)}{360 d^3}-\frac{b^4 f \sin (a) (d e-c f) \text{Ci}\left(\frac{b}{\sqrt{c+d x}}\right)}{6 d^3}-\frac{b^4 f \cos (a) (d e-c f) \text{Si}\left(\frac{b}{\sqrt{c+d x}}\right)}{6 d^3}+\frac{b^4 f^2 (c+d x) \sin \left(a+\frac{b}{\sqrt{c+d x}}\right)}{360 d^3}-\frac{b^3 f \sqrt{c+d x} (d e-c f) \cos \left(a+\frac{b}{\sqrt{c+d x}}\right)}{6 d^3}-\frac{b^3 f^2 (c+d x)^{3/2} \cos \left(a+\frac{b}{\sqrt{c+d x}}\right)}{180 d^3}+\frac{b^2 \sin (a) (d e-c f)^2 \text{Ci}\left(\frac{b}{\sqrt{c+d x}}\right)}{d^3}+\frac{b^2 \cos (a) (d e-c f)^2 \text{Si}\left(\frac{b}{\sqrt{c+d x}}\right)}{d^3}-\frac{b^2 f (c+d x) (d e-c f) \sin \left(a+\frac{b}{\sqrt{c+d x}}\right)}{6 d^3}-\frac{b^2 f^2 (c+d x)^2 \sin \left(a+\frac{b}{\sqrt{c+d x}}\right)}{60 d^3}+\frac{f (c+d x)^2 (d e-c f) \sin \left(a+\frac{b}{\sqrt{c+d x}}\right)}{d^3}+\frac{(c+d x) (d e-c f)^2 \sin \left(a+\frac{b}{\sqrt{c+d x}}\right)}{d^3}+\frac{b f (c+d x)^{3/2} (d e-c f) \cos \left(a+\frac{b}{\sqrt{c+d x}}\right)}{3 d^3}+\frac{b \sqrt{c+d x} (d e-c f)^2 \cos \left(a+\frac{b}{\sqrt{c+d x}}\right)}{d^3}+\frac{f^2 (c+d x)^3 \sin \left(a+\frac{b}{\sqrt{c+d x}}\right)}{3 d^3}+\frac{b f^2 (c+d x)^{5/2} \cos \left(a+\frac{b}{\sqrt{c+d x}}\right)}{15 d^3}",1,"((I/720)*((Sqrt[c + d*x]*((-I)*b^5*f^2 + b^4*f^2*Sqrt[c + d*x] + (2*I)*b^3*f*(30*d*e - 29*c*f + d*f*x) - 6*b^2*f*Sqrt[c + d*x]*(10*d*e - 9*c*f + d*f*x) + 120*Sqrt[c + d*x]*(c^2*f^2 - c*d*f*(3*e + f*x) + d^2*(3*e^2 + 3*e*f*x + f^2*x^2)) - (24*I)*b*(11*c^2*f^2 - c*d*f*(25*e + 3*f*x) + d^2*(15*e^2 + 5*e*f*x + f^2*x^2))))/E^((I*b)/Sqrt[c + d*x]) - E^(I*(2*a + b/Sqrt[c + d*x]))*Sqrt[c + d*x]*(I*b^5*f^2 + b^4*f^2*Sqrt[c + d*x] - (2*I)*b^3*f*(30*d*e - 29*c*f + d*f*x) - 6*b^2*f*Sqrt[c + d*x]*(10*d*e - 9*c*f + d*f*x) + 120*Sqrt[c + d*x]*(c^2*f^2 - c*d*f*(3*e + f*x) + d^2*(3*e^2 + 3*e*f*x + f^2*x^2)) + (24*I)*b*(11*c^2*f^2 - c*d*f*(25*e + 3*f*x) + d^2*(15*e^2 + 5*e*f*x + f^2*x^2))) + b^2*(360*d^2*e^2 - 60*(b^2 + 12*c)*d*e*f + (b^4 + 60*b^2*c + 360*c^2)*f^2)*ExpIntegralEi[((-I)*b)/Sqrt[c + d*x]] - b^2*E^((2*I)*a)*(360*d^2*e^2 - 60*(b^2 + 12*c)*d*e*f + (b^4 + 60*b^2*c + 360*c^2)*f^2)*ExpIntegralEi[(I*b)/Sqrt[c + d*x]]))/(d^3*E^(I*a))","C",1
198,1,367,301,0.6424682,"\int (e+f x) \sin \left(a+\frac{b}{\sqrt{c+d x}}\right) \, dx","Integrate[(e + f*x)*Sin[a + b/Sqrt[c + d*x]],x]","-\frac{b^2 f \left(b^2+12 c\right) \left(\sin (a) \text{Ci}\left(\frac{b}{\sqrt{c+d x}}\right)+\cos (a) \text{Si}\left(\frac{b}{\sqrt{c+d x}}\right)\right)}{12 d^2}+\frac{b^2 e \left(\sin (a) \text{Ci}\left(\frac{b}{\sqrt{c+d x}}\right)+\cos (a) \text{Si}\left(\frac{b}{\sqrt{c+d x}}\right)\right)}{d}+\frac{f \sqrt{c+d x} \cos \left(\frac{b}{\sqrt{c+d x}}\right) \left(b^3 (-\cos (a))-b^2 \sin (a) \sqrt{c+d x}+2 b \cos (a) (c+d x)-12 b c \cos (a)+6 \sin (a) (c+d x)^{3/2}-12 c \sin (a) \sqrt{c+d x}\right)}{12 d^2}+\frac{f \sqrt{c+d x} \sin \left(\frac{b}{\sqrt{c+d x}}\right) \left(b^3 \sin (a)-b^2 \cos (a) \sqrt{c+d x}-2 b \sin (a) (c+d x)+12 b c \sin (a)+6 \cos (a) (c+d x)^{3/2}-12 c \cos (a) \sqrt{c+d x}\right)}{12 d^2}+\frac{e \sqrt{c+d x} \cos \left(\frac{b}{\sqrt{c+d x}}\right) \left(b \cos (a)+\sin (a) \sqrt{c+d x}\right)}{d}+\frac{e \sqrt{c+d x} \sin \left(\frac{b}{\sqrt{c+d x}}\right) \left(\cos (a) \sqrt{c+d x}-b \sin (a)\right)}{d}","-\frac{b^4 f \sin (a) \text{Ci}\left(\frac{b}{\sqrt{c+d x}}\right)}{12 d^2}-\frac{b^4 f \cos (a) \text{Si}\left(\frac{b}{\sqrt{c+d x}}\right)}{12 d^2}-\frac{b^3 f \sqrt{c+d x} \cos \left(a+\frac{b}{\sqrt{c+d x}}\right)}{12 d^2}+\frac{b^2 \sin (a) (d e-c f) \text{Ci}\left(\frac{b}{\sqrt{c+d x}}\right)}{d^2}+\frac{b^2 \cos (a) (d e-c f) \text{Si}\left(\frac{b}{\sqrt{c+d x}}\right)}{d^2}-\frac{b^2 f (c+d x) \sin \left(a+\frac{b}{\sqrt{c+d x}}\right)}{12 d^2}+\frac{(c+d x) (d e-c f) \sin \left(a+\frac{b}{\sqrt{c+d x}}\right)}{d^2}+\frac{b \sqrt{c+d x} (d e-c f) \cos \left(a+\frac{b}{\sqrt{c+d x}}\right)}{d^2}+\frac{f (c+d x)^2 \sin \left(a+\frac{b}{\sqrt{c+d x}}\right)}{2 d^2}+\frac{b f (c+d x)^{3/2} \cos \left(a+\frac{b}{\sqrt{c+d x}}\right)}{6 d^2}",1,"(e*Sqrt[c + d*x]*Cos[b/Sqrt[c + d*x]]*(b*Cos[a] + Sqrt[c + d*x]*Sin[a]))/d + (f*Sqrt[c + d*x]*Cos[b/Sqrt[c + d*x]]*(-(b^3*Cos[a]) - 12*b*c*Cos[a] + 2*b*(c + d*x)*Cos[a] - b^2*Sqrt[c + d*x]*Sin[a] - 12*c*Sqrt[c + d*x]*Sin[a] + 6*(c + d*x)^(3/2)*Sin[a]))/(12*d^2) + (e*Sqrt[c + d*x]*(Sqrt[c + d*x]*Cos[a] - b*Sin[a])*Sin[b/Sqrt[c + d*x]])/d + (f*Sqrt[c + d*x]*(-(b^2*Sqrt[c + d*x]*Cos[a]) - 12*c*Sqrt[c + d*x]*Cos[a] + 6*(c + d*x)^(3/2)*Cos[a] + b^3*Sin[a] + 12*b*c*Sin[a] - 2*b*(c + d*x)*Sin[a])*Sin[b/Sqrt[c + d*x]])/(12*d^2) + (b^2*e*(CosIntegral[b/Sqrt[c + d*x]]*Sin[a] + Cos[a]*SinIntegral[b/Sqrt[c + d*x]]))/d - (b^2*(b^2 + 12*c)*f*(CosIntegral[b/Sqrt[c + d*x]]*Sin[a] + Cos[a]*SinIntegral[b/Sqrt[c + d*x]]))/(12*d^2)","A",1
199,1,99,94,0.085562,"\int \sin \left(a+\frac{b}{\sqrt{c+d x}}\right) \, dx","Integrate[Sin[a + b/Sqrt[c + d*x]],x]","\frac{b^2 \sin (a) \text{Ci}\left(\frac{b}{\sqrt{c+d x}}\right)+b^2 \cos (a) \text{Si}\left(\frac{b}{\sqrt{c+d x}}\right)+c \sin \left(a+\frac{b}{\sqrt{c+d x}}\right)+d x \sin \left(a+\frac{b}{\sqrt{c+d x}}\right)+b \sqrt{c+d x} \cos \left(a+\frac{b}{\sqrt{c+d x}}\right)}{d}","\frac{b^2 \sin (a) \text{Ci}\left(\frac{b}{\sqrt{c+d x}}\right)}{d}+\frac{b^2 \cos (a) \text{Si}\left(\frac{b}{\sqrt{c+d x}}\right)}{d}+\frac{(c+d x) \sin \left(a+\frac{b}{\sqrt{c+d x}}\right)}{d}+\frac{b \sqrt{c+d x} \cos \left(a+\frac{b}{\sqrt{c+d x}}\right)}{d}",1,"(b*Sqrt[c + d*x]*Cos[a + b/Sqrt[c + d*x]] + b^2*CosIntegral[b/Sqrt[c + d*x]]*Sin[a] + c*Sin[a + b/Sqrt[c + d*x]] + d*x*Sin[a + b/Sqrt[c + d*x]] + b^2*Cos[a]*SinIntegral[b/Sqrt[c + d*x]])/d","A",1
200,0,0,276,15.6885259,"\int \frac{\sin \left(a+\frac{b}{\sqrt{c+d x}}\right)}{e+f x} \, dx","Integrate[Sin[a + b/Sqrt[c + d*x]]/(e + f*x),x]","\int \frac{\sin \left(a+\frac{b}{\sqrt{c+d x}}\right)}{e+f x} \, dx","\frac{\sin \left(a-\frac{b \sqrt{f}}{\sqrt{c f-d e}}\right) \text{Ci}\left(\frac{\sqrt{f} b}{\sqrt{c f-d e}}+\frac{b}{\sqrt{c+d x}}\right)}{f}+\frac{\sin \left(a+\frac{b \sqrt{f}}{\sqrt{c f-d e}}\right) \text{Ci}\left(\frac{b \sqrt{f}}{\sqrt{c f-d e}}-\frac{b}{\sqrt{c+d x}}\right)}{f}-\frac{2 \sin (a) \text{Ci}\left(\frac{b}{\sqrt{c+d x}}\right)}{f}-\frac{\cos \left(a+\frac{b \sqrt{f}}{\sqrt{c f-d e}}\right) \text{Si}\left(\frac{b \sqrt{f}}{\sqrt{c f-d e}}-\frac{b}{\sqrt{c+d x}}\right)}{f}+\frac{\cos \left(a-\frac{b \sqrt{f}}{\sqrt{c f-d e}}\right) \text{Si}\left(\frac{\sqrt{f} b}{\sqrt{c f-d e}}+\frac{b}{\sqrt{c+d x}}\right)}{f}-\frac{2 \cos (a) \text{Si}\left(\frac{b}{\sqrt{c+d x}}\right)}{f}",1,"Integrate[Sin[a + b/Sqrt[c + d*x]]/(e + f*x), x]","F",-1
201,-1,0,350,180.033636,"\int \frac{\sin \left(a+\frac{b}{\sqrt{c+d x}}\right)}{(e+f x)^2} \, dx","Integrate[Sin[a + b/Sqrt[c + d*x]]/(e + f*x)^2,x]","\text{\$Aborted}","-\frac{b d \cos \left(a+\frac{b \sqrt{f}}{\sqrt{c f-d e}}\right) \text{Ci}\left(\frac{b \sqrt{f}}{\sqrt{c f-d e}}-\frac{b}{\sqrt{c+d x}}\right)}{2 \sqrt{f} (c f-d e)^{3/2}}+\frac{b d \cos \left(a-\frac{b \sqrt{f}}{\sqrt{c f-d e}}\right) \text{Ci}\left(\frac{\sqrt{f} b}{\sqrt{c f-d e}}+\frac{b}{\sqrt{c+d x}}\right)}{2 \sqrt{f} (c f-d e)^{3/2}}-\frac{b d \sin \left(a+\frac{b \sqrt{f}}{\sqrt{c f-d e}}\right) \text{Si}\left(\frac{b \sqrt{f}}{\sqrt{c f-d e}}-\frac{b}{\sqrt{c+d x}}\right)}{2 \sqrt{f} (c f-d e)^{3/2}}-\frac{b d \sin \left(a-\frac{b \sqrt{f}}{\sqrt{c f-d e}}\right) \text{Si}\left(\frac{\sqrt{f} b}{\sqrt{c f-d e}}+\frac{b}{\sqrt{c+d x}}\right)}{2 \sqrt{f} (c f-d e)^{3/2}}+\frac{(c+d x) \sin \left(a+\frac{b}{\sqrt{c+d x}}\right)}{(e+f x) (d e-c f)}",1,"$Aborted","F",-1
202,1,463,390,2.2826258,"\int (e+f x)^2 \sin \left(a+\frac{b}{(c+d x)^{3/2}}\right) \, dx","Integrate[(e + f*x)^2*Sin[a + b/(c + d*x)^(3/2)],x]","\frac{i \left((\cos (a)-i \sin (a)) \left(4 f (c+d x)^2 \left(\frac{i b}{(c+d x)^{3/2}}\right)^{4/3} (d e-c f) \Gamma \left(-\frac{4}{3},\frac{i b}{(c+d x)^{3/2}}\right)+2 (c+d x) \left(\frac{i b}{(c+d x)^{3/2}}\right)^{2/3} (d e-c f)^2 \Gamma \left(-\frac{2}{3},\frac{i b}{(c+d x)^{3/2}}\right)-i b f^2 \left(i b \text{Ei}\left(-\frac{i b}{(c+d x)^{3/2}}\right)+(c+d x)^{3/2} \left(\cos \left(\frac{b}{(c+d x)^{3/2}}\right)-i \sin \left(\frac{b}{(c+d x)^{3/2}}\right)\right)\right)+f^2 (c+d x)^3 \left(\cos \left(\frac{b}{(c+d x)^{3/2}}\right)-i \sin \left(\frac{b}{(c+d x)^{3/2}}\right)\right)\right)-(\cos (a)+i \sin (a)) \left(b^2 f^2 \text{Ei}\left(\frac{i b}{(c+d x)^{3/2}}\right)+4 f (c+d x)^2 \left(-\frac{i b}{(c+d x)^{3/2}}\right)^{4/3} (d e-c f) \Gamma \left(-\frac{4}{3},-\frac{i b}{(c+d x)^{3/2}}\right)+2 (c+d x) \left(-\frac{i b}{(c+d x)^{3/2}}\right)^{2/3} (d e-c f)^2 \Gamma \left(-\frac{2}{3},-\frac{i b}{(c+d x)^{3/2}}\right)+f^2 (c+d x)^3 \left(\cos \left(\frac{b}{(c+d x)^{3/2}}\right)+i \sin \left(\frac{b}{(c+d x)^{3/2}}\right)\right)+i b f^2 (c+d x)^{3/2} \left(\cos \left(\frac{b}{(c+d x)^{3/2}}\right)+i \sin \left(\frac{b}{(c+d x)^{3/2}}\right)\right)\right)\right)}{6 d^3}","\frac{b^2 f^2 \sin (a) \text{Ci}\left(\frac{b}{(c+d x)^{3/2}}\right)}{3 d^3}+\frac{b^2 f^2 \cos (a) \text{Si}\left(\frac{b}{(c+d x)^{3/2}}\right)}{3 d^3}-\frac{2 i e^{i a} f (c+d x)^2 \left(-\frac{i b}{(c+d x)^{3/2}}\right)^{4/3} (d e-c f) \Gamma \left(-\frac{4}{3},-\frac{i b}{(c+d x)^{3/2}}\right)}{3 d^3}+\frac{2 i e^{-i a} f (c+d x)^2 \left(\frac{i b}{(c+d x)^{3/2}}\right)^{4/3} (d e-c f) \Gamma \left(-\frac{4}{3},\frac{i b}{(c+d x)^{3/2}}\right)}{3 d^3}-\frac{i e^{i a} (c+d x) \left(-\frac{i b}{(c+d x)^{3/2}}\right)^{2/3} (d e-c f)^2 \Gamma \left(-\frac{2}{3},-\frac{i b}{(c+d x)^{3/2}}\right)}{3 d^3}+\frac{i e^{-i a} (c+d x) \left(\frac{i b}{(c+d x)^{3/2}}\right)^{2/3} (d e-c f)^2 \Gamma \left(-\frac{2}{3},\frac{i b}{(c+d x)^{3/2}}\right)}{3 d^3}+\frac{f^2 (c+d x)^3 \sin \left(a+\frac{b}{(c+d x)^{3/2}}\right)}{3 d^3}+\frac{b f^2 (c+d x)^{3/2} \cos \left(a+\frac{b}{(c+d x)^{3/2}}\right)}{3 d^3}",1,"((I/6)*((Cos[a] - I*Sin[a])*(4*f*(d*e - c*f)*((I*b)/(c + d*x)^(3/2))^(4/3)*(c + d*x)^2*Gamma[-4/3, (I*b)/(c + d*x)^(3/2)] + 2*(d*e - c*f)^2*((I*b)/(c + d*x)^(3/2))^(2/3)*(c + d*x)*Gamma[-2/3, (I*b)/(c + d*x)^(3/2)] - I*b*f^2*(I*b*ExpIntegralEi[((-I)*b)/(c + d*x)^(3/2)] + (c + d*x)^(3/2)*(Cos[b/(c + d*x)^(3/2)] - I*Sin[b/(c + d*x)^(3/2)])) + f^2*(c + d*x)^3*(Cos[b/(c + d*x)^(3/2)] - I*Sin[b/(c + d*x)^(3/2)])) - (Cos[a] + I*Sin[a])*(b^2*f^2*ExpIntegralEi[(I*b)/(c + d*x)^(3/2)] + 4*f*(d*e - c*f)*(((-I)*b)/(c + d*x)^(3/2))^(4/3)*(c + d*x)^2*Gamma[-4/3, ((-I)*b)/(c + d*x)^(3/2)] + 2*(d*e - c*f)^2*(((-I)*b)/(c + d*x)^(3/2))^(2/3)*(c + d*x)*Gamma[-2/3, ((-I)*b)/(c + d*x)^(3/2)] + I*b*f^2*(c + d*x)^(3/2)*(Cos[b/(c + d*x)^(3/2)] + I*Sin[b/(c + d*x)^(3/2)]) + f^2*(c + d*x)^3*(Cos[b/(c + d*x)^(3/2)] + I*Sin[b/(c + d*x)^(3/2)]))))/d^3","A",1
203,1,835,251,2.7708035,"\int (e+f x) \sin \left(a+\frac{b}{(c+d x)^{3/2}}\right) \, dx","Integrate[(e + f*x)*Sin[a + b/(c + d*x)^(3/2)],x]","\frac{9 i f \cos (a) \left(\frac{2 \Gamma \left(\frac{2}{3},-\frac{i b}{(c+d x)^{3/2}}\right)}{3 \left(-\frac{i b}{(c+d x)^{3/2}}\right)^{2/3} (c+d x)}-\frac{2 \Gamma \left(\frac{2}{3},\frac{i b}{(c+d x)^{3/2}}\right)}{3 \left(\frac{i b}{(c+d x)^{3/2}}\right)^{2/3} (c+d x)}\right) b^2}{8 d^2}-\frac{9 f \left(\frac{2 \Gamma \left(\frac{2}{3},-\frac{i b}{(c+d x)^{3/2}}\right)}{3 \left(-\frac{i b}{(c+d x)^{3/2}}\right)^{2/3} (c+d x)}+\frac{2 \Gamma \left(\frac{2}{3},\frac{i b}{(c+d x)^{3/2}}\right)}{3 \left(\frac{i b}{(c+d x)^{3/2}}\right)^{2/3} (c+d x)}\right) \sin (a) b^2}{8 d^2}+\frac{3 e \cos (a) \left(\frac{2 \Gamma \left(\frac{1}{3},-\frac{i b}{(c+d x)^{3/2}}\right)}{3 \sqrt[3]{-\frac{i b}{(c+d x)^{3/2}}} \sqrt{c+d x}}+\frac{2 \Gamma \left(\frac{1}{3},\frac{i b}{(c+d x)^{3/2}}\right)}{3 \sqrt[3]{\frac{i b}{(c+d x)^{3/2}}} \sqrt{c+d x}}\right) b}{4 d}-\frac{3 c f \cos (a) \left(\frac{2 \Gamma \left(\frac{1}{3},-\frac{i b}{(c+d x)^{3/2}}\right)}{3 \sqrt[3]{-\frac{i b}{(c+d x)^{3/2}}} \sqrt{c+d x}}+\frac{2 \Gamma \left(\frac{1}{3},\frac{i b}{(c+d x)^{3/2}}\right)}{3 \sqrt[3]{\frac{i b}{(c+d x)^{3/2}}} \sqrt{c+d x}}\right) b}{4 d^2}+\frac{3 i e \left(\frac{2 \Gamma \left(\frac{1}{3},-\frac{i b}{(c+d x)^{3/2}}\right)}{3 \sqrt[3]{-\frac{i b}{(c+d x)^{3/2}}} \sqrt{c+d x}}-\frac{2 \Gamma \left(\frac{1}{3},\frac{i b}{(c+d x)^{3/2}}\right)}{3 \sqrt[3]{\frac{i b}{(c+d x)^{3/2}}} \sqrt{c+d x}}\right) \sin (a) b}{4 d}-\frac{3 i c f \left(\frac{2 \Gamma \left(\frac{1}{3},-\frac{i b}{(c+d x)^{3/2}}\right)}{3 \sqrt[3]{-\frac{i b}{(c+d x)^{3/2}}} \sqrt{c+d x}}-\frac{2 \Gamma \left(\frac{1}{3},\frac{i b}{(c+d x)^{3/2}}\right)}{3 \sqrt[3]{\frac{i b}{(c+d x)^{3/2}}} \sqrt{c+d x}}\right) \sin (a) b}{4 d^2}+\frac{e (c+d x) \cos \left(\frac{b}{(c+d x)^{3/2}}\right) \sin (a)}{d}+\frac{f \sqrt{c+d x} \cos \left(\frac{b}{(c+d x)^{3/2}}\right) \left(\sin (a) (c+d x)^{3/2}-2 c \sin (a) \sqrt{c+d x}+3 b \cos (a)\right)}{2 d^2}+\frac{e (c+d x) \cos (a) \sin \left(\frac{b}{(c+d x)^{3/2}}\right)}{d}+\frac{f \sqrt{c+d x} \left(\cos (a) (c+d x)^{3/2}-2 c \cos (a) \sqrt{c+d x}-3 b \sin (a)\right) \sin \left(\frac{b}{(c+d x)^{3/2}}\right)}{2 d^2}","-\frac{i e^{i a} (c+d x) \left(-\frac{i b}{(c+d x)^{3/2}}\right)^{2/3} (d e-c f) \Gamma \left(-\frac{2}{3},-\frac{i b}{(c+d x)^{3/2}}\right)}{3 d^2}+\frac{i e^{-i a} (c+d x) \left(\frac{i b}{(c+d x)^{3/2}}\right)^{2/3} (d e-c f) \Gamma \left(-\frac{2}{3},\frac{i b}{(c+d x)^{3/2}}\right)}{3 d^2}-\frac{i e^{i a} f (c+d x)^2 \left(-\frac{i b}{(c+d x)^{3/2}}\right)^{4/3} \Gamma \left(-\frac{4}{3},-\frac{i b}{(c+d x)^{3/2}}\right)}{3 d^2}+\frac{i e^{-i a} f (c+d x)^2 \left(\frac{i b}{(c+d x)^{3/2}}\right)^{4/3} \Gamma \left(-\frac{4}{3},\frac{i b}{(c+d x)^{3/2}}\right)}{3 d^2}",1,"(3*b*e*Cos[a]*((2*Gamma[1/3, ((-I)*b)/(c + d*x)^(3/2)])/(3*(((-I)*b)/(c + d*x)^(3/2))^(1/3)*Sqrt[c + d*x]) + (2*Gamma[1/3, (I*b)/(c + d*x)^(3/2)])/(3*((I*b)/(c + d*x)^(3/2))^(1/3)*Sqrt[c + d*x])))/(4*d) - (3*b*c*f*Cos[a]*((2*Gamma[1/3, ((-I)*b)/(c + d*x)^(3/2)])/(3*(((-I)*b)/(c + d*x)^(3/2))^(1/3)*Sqrt[c + d*x]) + (2*Gamma[1/3, (I*b)/(c + d*x)^(3/2)])/(3*((I*b)/(c + d*x)^(3/2))^(1/3)*Sqrt[c + d*x])))/(4*d^2) + (((9*I)/8)*b^2*f*Cos[a]*((2*Gamma[2/3, ((-I)*b)/(c + d*x)^(3/2)])/(3*(((-I)*b)/(c + d*x)^(3/2))^(2/3)*(c + d*x)) - (2*Gamma[2/3, (I*b)/(c + d*x)^(3/2)])/(3*((I*b)/(c + d*x)^(3/2))^(2/3)*(c + d*x))))/d^2 + (e*(c + d*x)*Cos[b/(c + d*x)^(3/2)]*Sin[a])/d + (((3*I)/4)*b*e*((2*Gamma[1/3, ((-I)*b)/(c + d*x)^(3/2)])/(3*(((-I)*b)/(c + d*x)^(3/2))^(1/3)*Sqrt[c + d*x]) - (2*Gamma[1/3, (I*b)/(c + d*x)^(3/2)])/(3*((I*b)/(c + d*x)^(3/2))^(1/3)*Sqrt[c + d*x]))*Sin[a])/d - (((3*I)/4)*b*c*f*((2*Gamma[1/3, ((-I)*b)/(c + d*x)^(3/2)])/(3*(((-I)*b)/(c + d*x)^(3/2))^(1/3)*Sqrt[c + d*x]) - (2*Gamma[1/3, (I*b)/(c + d*x)^(3/2)])/(3*((I*b)/(c + d*x)^(3/2))^(1/3)*Sqrt[c + d*x]))*Sin[a])/d^2 - (9*b^2*f*((2*Gamma[2/3, ((-I)*b)/(c + d*x)^(3/2)])/(3*(((-I)*b)/(c + d*x)^(3/2))^(2/3)*(c + d*x)) + (2*Gamma[2/3, (I*b)/(c + d*x)^(3/2)])/(3*((I*b)/(c + d*x)^(3/2))^(2/3)*(c + d*x)))*Sin[a])/(8*d^2) + (f*Sqrt[c + d*x]*Cos[b/(c + d*x)^(3/2)]*(3*b*Cos[a] - 2*c*Sqrt[c + d*x]*Sin[a] + (c + d*x)^(3/2)*Sin[a]))/(2*d^2) + (e*(c + d*x)*Cos[a]*Sin[b/(c + d*x)^(3/2)])/d + (f*Sqrt[c + d*x]*(-2*c*Sqrt[c + d*x]*Cos[a] + (c + d*x)^(3/2)*Cos[a] - 3*b*Sin[a])*Sin[b/(c + d*x)^(3/2)])/(2*d^2)","B",1
204,1,166,115,0.4491189,"\int \sin \left(a+\frac{b}{(c+d x)^{3/2}}\right) \, dx","Integrate[Sin[a + b/(c + d*x)^(3/2)],x]","\frac{2 (c+d x)^{3/2} \sqrt[3]{\frac{b^2}{(c+d x)^3}} \sin \left(a+\frac{b}{(c+d x)^{3/2}}\right)+b (\cos (a)-i \sin (a)) \sqrt[3]{-\frac{i b}{(c+d x)^{3/2}}} \Gamma \left(\frac{1}{3},\frac{i b}{(c+d x)^{3/2}}\right)+b (\cos (a)+i \sin (a)) \sqrt[3]{\frac{i b}{(c+d x)^{3/2}}} \Gamma \left(\frac{1}{3},-\frac{i b}{(c+d x)^{3/2}}\right)}{2 d \sqrt{c+d x} \sqrt[3]{\frac{b^2}{(c+d x)^3}}}","\frac{i e^{-i a} (c+d x) \left(\frac{i b}{(c+d x)^{3/2}}\right)^{2/3} \Gamma \left(-\frac{2}{3},\frac{i b}{(c+d x)^{3/2}}\right)}{3 d}-\frac{i e^{i a} (c+d x) \left(-\frac{i b}{(c+d x)^{3/2}}\right)^{2/3} \Gamma \left(-\frac{2}{3},-\frac{i b}{(c+d x)^{3/2}}\right)}{3 d}",1,"(b*(((-I)*b)/(c + d*x)^(3/2))^(1/3)*Gamma[1/3, (I*b)/(c + d*x)^(3/2)]*(Cos[a] - I*Sin[a]) + b*((I*b)/(c + d*x)^(3/2))^(1/3)*Gamma[1/3, ((-I)*b)/(c + d*x)^(3/2)]*(Cos[a] + I*Sin[a]) + 2*(b^2/(c + d*x)^3)^(1/3)*(c + d*x)^(3/2)*Sin[a + b/(c + d*x)^(3/2)])/(2*d*(b^2/(c + d*x)^3)^(1/3)*Sqrt[c + d*x])","A",1
205,0,0,25,13.3801904,"\int \frac{\sin \left(a+\frac{b}{(c+d x)^{3/2}}\right)}{e+f x} \, dx","Integrate[Sin[a + b/(c + d*x)^(3/2)]/(e + f*x),x]","\int \frac{\sin \left(a+\frac{b}{(c+d x)^{3/2}}\right)}{e+f x} \, dx","\text{Int}\left(\frac{\sin \left(a+\frac{b}{(c+d x)^{3/2}}\right)}{e+f x},x\right)",0,"Integrate[Sin[a + b/(c + d*x)^(3/2)]/(e + f*x), x]","A",-1
206,0,0,25,15.8967038,"\int \frac{\sin \left(a+\frac{b}{(c+d x)^{3/2}}\right)}{(e+f x)^2} \, dx","Integrate[Sin[a + b/(c + d*x)^(3/2)]/(e + f*x)^2,x]","\int \frac{\sin \left(a+\frac{b}{(c+d x)^{3/2}}\right)}{(e+f x)^2} \, dx","\text{Int}\left(\frac{\sin \left(a+\frac{b}{(c+d x)^{3/2}}\right)}{(e+f x)^2},x\right)",0,"Integrate[Sin[a + b/(c + d*x)^(3/2)]/(e + f*x)^2, x]","A",-1
207,1,256,633,2.6546621,"\int (e+f x)^2 \sin \left(a+b \sqrt[3]{c+d x}\right) \, dx","Integrate[(e + f*x)^2*Sin[a + b*(c + d*x)^(1/3)],x]","\frac{6 b \sin \left(a+b \sqrt[3]{c+d x}\right) \left(b^6 d \sqrt[3]{c+d x} (e+f x) (3 c f+d (e+4 f x))-12 b^4 f (c+d x)^{2/3} (9 c f+5 d e+14 d f x)+120 b^2 f (27 c f+d (e+28 f x))-20160 f^2 \sqrt[3]{c+d x}\right)-3 \cos \left(a+b \sqrt[3]{c+d x}\right) \left(b^8 d^2 (c+d x)^{2/3} (e+f x)^2-2 b^6 \left(9 c^2 f^2+18 c d f (e+2 f x)+d^2 \left(e^2+20 e f x+28 f^2 x^2\right)\right)+240 b^4 f \sqrt[3]{c+d x} (6 c f+d (e+7 f x))-20160 b^2 f^2 (c+d x)^{2/3}+40320 f^2\right)}{b^9 d^3}","-\frac{120960 f^2 \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^9 d^3}-\frac{120960 f^2 \sqrt[3]{c+d x} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^8 d^3}+\frac{60480 f^2 (c+d x)^{2/3} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^7 d^3}+\frac{720 f (d e-c f) \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^6 d^3}+\frac{20160 f^2 (c+d x) \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^6 d^3}-\frac{720 f \sqrt[3]{c+d x} (d e-c f) \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^5 d^3}-\frac{5040 f^2 (c+d x)^{4/3} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^5 d^3}-\frac{360 f (c+d x)^{2/3} (d e-c f) \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^4 d^3}-\frac{1008 f^2 (c+d x)^{5/3} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^4 d^3}+\frac{120 f (c+d x) (d e-c f) \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d^3}+\frac{6 (d e-c f)^2 \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d^3}+\frac{168 f^2 (c+d x)^2 \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d^3}+\frac{30 f (c+d x)^{4/3} (d e-c f) \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d^3}+\frac{6 \sqrt[3]{c+d x} (d e-c f)^2 \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d^3}+\frac{24 f^2 (c+d x)^{7/3} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d^3}-\frac{6 f (c+d x)^{5/3} (d e-c f) \cos \left(a+b \sqrt[3]{c+d x}\right)}{b d^3}-\frac{3 (c+d x)^{2/3} (d e-c f)^2 \cos \left(a+b \sqrt[3]{c+d x}\right)}{b d^3}-\frac{3 f^2 (c+d x)^{8/3} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b d^3}",1,"(-3*(40320*f^2 - 20160*b^2*f^2*(c + d*x)^(2/3) + b^8*d^2*(c + d*x)^(2/3)*(e + f*x)^2 + 240*b^4*f*(c + d*x)^(1/3)*(6*c*f + d*(e + 7*f*x)) - 2*b^6*(9*c^2*f^2 + 18*c*d*f*(e + 2*f*x) + d^2*(e^2 + 20*e*f*x + 28*f^2*x^2)))*Cos[a + b*(c + d*x)^(1/3)] + 6*b*(-20160*f^2*(c + d*x)^(1/3) - 12*b^4*f*(c + d*x)^(2/3)*(5*d*e + 9*c*f + 14*d*f*x) + b^6*d*(c + d*x)^(1/3)*(e + f*x)*(3*c*f + d*(e + 4*f*x)) + 120*b^2*f*(27*c*f + d*(e + 28*f*x)))*Sin[a + b*(c + d*x)^(1/3)])/(b^9*d^3)","A",1
208,1,147,288,0.6461062,"\int (e+f x) \sin \left(a+b \sqrt[3]{c+d x}\right) \, dx","Integrate[(e + f*x)*Sin[a + b*(c + d*x)^(1/3)],x]","\frac{3 \sin \left(a+b \sqrt[3]{c+d x}\right) \left(2 b^4 d e \sqrt[3]{c+d x}+f \left(b^4 \sqrt[3]{c+d x} (3 c+5 d x)-60 b^2 (c+d x)^{2/3}+120\right)\right)-3 b \cos \left(a+b \sqrt[3]{c+d x}\right) \left(b^4 d (c+d x)^{2/3} (e+f x)-2 b^2 (9 c f+d (e+10 f x))+120 f \sqrt[3]{c+d x}\right)}{b^6 d^2}","\frac{360 f \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^6 d^2}-\frac{360 f \sqrt[3]{c+d x} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^5 d^2}-\frac{180 f (c+d x)^{2/3} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^4 d^2}+\frac{6 (d e-c f) \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d^2}+\frac{60 f (c+d x) \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d^2}+\frac{6 \sqrt[3]{c+d x} (d e-c f) \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d^2}+\frac{15 f (c+d x)^{4/3} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d^2}-\frac{3 (c+d x)^{2/3} (d e-c f) \cos \left(a+b \sqrt[3]{c+d x}\right)}{b d^2}-\frac{3 f (c+d x)^{5/3} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b d^2}",1,"(-3*b*(120*f*(c + d*x)^(1/3) + b^4*d*(c + d*x)^(2/3)*(e + f*x) - 2*b^2*(9*c*f + d*(e + 10*f*x)))*Cos[a + b*(c + d*x)^(1/3)] + 3*(2*b^4*d*e*(c + d*x)^(1/3) + f*(120 - 60*b^2*(c + d*x)^(2/3) + b^4*(c + d*x)^(1/3)*(3*c + 5*d*x)))*Sin[a + b*(c + d*x)^(1/3)])/(b^6*d^2)","A",1
209,1,65,85,0.1106853,"\int \sin \left(a+b \sqrt[3]{c+d x}\right) \, dx","Integrate[Sin[a + b*(c + d*x)^(1/3)],x]","\frac{\left(6-3 b^2 (c+d x)^{2/3}\right) \cos \left(a+b \sqrt[3]{c+d x}\right)+6 b \sqrt[3]{c+d x} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d}","\frac{6 \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d}+\frac{6 \sqrt[3]{c+d x} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d}-\frac{3 (c+d x)^{2/3} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b d}",1,"((6 - 3*b^2*(c + d*x)^(2/3))*Cos[a + b*(c + d*x)^(1/3)] + 6*b*(c + d*x)^(1/3)*Sin[a + b*(c + d*x)^(1/3)])/(b^3*d)","A",1
210,1,118,396,1.8481971,"\int \frac{\sin \left(a+b \sqrt[3]{c+d x}\right)}{e+f x} \, dx","Integrate[Sin[a + b*(c + d*x)^(1/3)]/(e + f*x),x]","\frac{i \left(\text{RootSum}\left[\text{$\#$1}^3 f-c f+d e\&,e^{-i \text{$\#$1} b-i a} \text{Ei}\left(-i b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)\&\right]-\text{RootSum}\left[\text{$\#$1}^3 f-c f+d e\&,e^{i \text{$\#$1} b+i a} \text{Ei}\left(i b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)\&\right]\right)}{2 f}","\frac{\sin \left(a-\frac{b \sqrt[3]{d e-c f}}{\sqrt[3]{f}}\right) \text{Ci}\left(\frac{\sqrt[3]{d e-c f} b}{\sqrt[3]{f}}+\sqrt[3]{c+d x} b\right)}{f}+\frac{\sin \left(a+\frac{\sqrt[3]{-1} b \sqrt[3]{d e-c f}}{\sqrt[3]{f}}\right) \text{Ci}\left(\frac{\sqrt[3]{-1} b \sqrt[3]{d e-c f}}{\sqrt[3]{f}}-b \sqrt[3]{c+d x}\right)}{f}+\frac{\sin \left(a-\frac{(-1)^{2/3} b \sqrt[3]{d e-c f}}{\sqrt[3]{f}}\right) \text{Ci}\left(\frac{(-1)^{2/3} \sqrt[3]{d e-c f} b}{\sqrt[3]{f}}+\sqrt[3]{c+d x} b\right)}{f}-\frac{\cos \left(a+\frac{\sqrt[3]{-1} b \sqrt[3]{d e-c f}}{\sqrt[3]{f}}\right) \text{Si}\left(\frac{\sqrt[3]{-1} b \sqrt[3]{d e-c f}}{\sqrt[3]{f}}-b \sqrt[3]{c+d x}\right)}{f}+\frac{\cos \left(a-\frac{b \sqrt[3]{d e-c f}}{\sqrt[3]{f}}\right) \text{Si}\left(\frac{\sqrt[3]{d e-c f} b}{\sqrt[3]{f}}+\sqrt[3]{c+d x} b\right)}{f}+\frac{\cos \left(a-\frac{(-1)^{2/3} b \sqrt[3]{d e-c f}}{\sqrt[3]{f}}\right) \text{Si}\left(\frac{(-1)^{2/3} \sqrt[3]{d e-c f} b}{\sqrt[3]{f}}+\sqrt[3]{c+d x} b\right)}{f}",1,"((I/2)*(RootSum[d*e - c*f + f*#1^3 & , E^((-I)*a - I*b*#1)*ExpIntegralEi[(-I)*b*((c + d*x)^(1/3) - #1)] & ] - RootSum[d*e - c*f + f*#1^3 & , E^(I*a + I*b*#1)*ExpIntegralEi[I*b*((c + d*x)^(1/3) - #1)] & ]))/f","C",1
211,1,180,555,1.1889914,"\int \frac{\sin \left(a+b \sqrt[3]{c+d x}\right)}{(e+f x)^2} \, dx","Integrate[Sin[a + b*(c + d*x)^(1/3)]/(e + f*x)^2,x]","\frac{b d \text{RootSum}\left[\text{$\#$1}^3 f-c f+d e\&,\frac{e^{-i \text{$\#$1} b-i a} \text{Ei}\left(-i b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)}{\text{$\#$1}^2}\&\right]+b d \text{RootSum}\left[\text{$\#$1}^3 f-c f+d e\&,\frac{e^{i \text{$\#$1} b+i a} \text{Ei}\left(i b \left(\sqrt[3]{c+d x}-\text{$\#$1}\right)\right)}{\text{$\#$1}^2}\&\right]+\frac{3 i f e^{-i \left(a+b \sqrt[3]{c+d x}\right)} \left(-1+e^{2 i \left(a+b \sqrt[3]{c+d x}\right)}\right)}{e+f x}}{6 f^2}","-\frac{\sqrt[3]{-1} b d \cos \left(a+\frac{\sqrt[3]{-1} b \sqrt[3]{d e-c f}}{\sqrt[3]{f}}\right) \text{Ci}\left(\frac{\sqrt[3]{-1} b \sqrt[3]{d e-c f}}{\sqrt[3]{f}}-b \sqrt[3]{c+d x}\right)}{3 f^{4/3} (d e-c f)^{2/3}}+\frac{b d \cos \left(a-\frac{b \sqrt[3]{d e-c f}}{\sqrt[3]{f}}\right) \text{Ci}\left(\frac{\sqrt[3]{d e-c f} b}{\sqrt[3]{f}}+\sqrt[3]{c+d x} b\right)}{3 f^{4/3} (d e-c f)^{2/3}}+\frac{(-1)^{2/3} b d \cos \left(a-\frac{(-1)^{2/3} b \sqrt[3]{d e-c f}}{\sqrt[3]{f}}\right) \text{Ci}\left(\frac{(-1)^{2/3} \sqrt[3]{d e-c f} b}{\sqrt[3]{f}}+\sqrt[3]{c+d x} b\right)}{3 f^{4/3} (d e-c f)^{2/3}}-\frac{\sqrt[3]{-1} b d \sin \left(a+\frac{\sqrt[3]{-1} b \sqrt[3]{d e-c f}}{\sqrt[3]{f}}\right) \text{Si}\left(\frac{\sqrt[3]{-1} b \sqrt[3]{d e-c f}}{\sqrt[3]{f}}-b \sqrt[3]{c+d x}\right)}{3 f^{4/3} (d e-c f)^{2/3}}-\frac{b d \sin \left(a-\frac{b \sqrt[3]{d e-c f}}{\sqrt[3]{f}}\right) \text{Si}\left(\frac{\sqrt[3]{d e-c f} b}{\sqrt[3]{f}}+\sqrt[3]{c+d x} b\right)}{3 f^{4/3} (d e-c f)^{2/3}}-\frac{(-1)^{2/3} b d \sin \left(a-\frac{(-1)^{2/3} b \sqrt[3]{d e-c f}}{\sqrt[3]{f}}\right) \text{Si}\left(\frac{(-1)^{2/3} \sqrt[3]{d e-c f} b}{\sqrt[3]{f}}+\sqrt[3]{c+d x} b\right)}{3 f^{4/3} (d e-c f)^{2/3}}-\frac{\sin \left(a+b \sqrt[3]{c+d x}\right)}{f (e+f x)}",1,"(((3*I)*(-1 + E^((2*I)*(a + b*(c + d*x)^(1/3))))*f)/(E^(I*(a + b*(c + d*x)^(1/3)))*(e + f*x)) + b*d*RootSum[d*e - c*f + f*#1^3 & , (E^((-I)*a - I*b*#1)*ExpIntegralEi[(-I)*b*((c + d*x)^(1/3) - #1)])/#1^2 & ] + b*d*RootSum[d*e - c*f + f*#1^3 & , (E^(I*a + I*b*#1)*ExpIntegralEi[I*b*((c + d*x)^(1/3) - #1)])/#1^2 & ])/(6*f^2)","C",1
212,1,432,513,2.4140462,"\int (e+f x)^2 \sin \left(a+b (c+d x)^{2/3}\right) \, dx","Integrate[(e + f*x)^2*Sin[a + b*(c + d*x)^(2/3)],x]","-\frac{3 i \left(\left(\cos \left(a+b (c+d x)^{2/3}\right)-i \sin \left(a+b (c+d x)^{2/3}\right)\right) \left((1+i) \sqrt{\frac{\pi }{2}} \left(8 b^3 (d e-c f)^2+105 i f^2\right) \text{erf}\left(\frac{(1+i) \sqrt{b} \sqrt[3]{c+d x}}{\sqrt{2}}\right) \left(\cos \left(b (c+d x)^{2/3}\right)+i \sin \left(b (c+d x)^{2/3}\right)\right)+2 \sqrt{b} \left(-8 i b^3 d^2 \sqrt[3]{c+d x} (e+f x)^2+4 b^2 f (c+d x)^{2/3} (c f-8 d e-7 d f x)+2 i b f (19 c f+16 d e+35 d f x)+105 f^2 \sqrt[3]{c+d x}\right)\right)+(\cos (a)+i \sin (a)) \left((1+i) \sqrt{\frac{\pi }{2}} \left(8 b^3 (d e-c f)^2-105 i f^2\right) \text{erfi}\left(\frac{(1+i) \sqrt{b} \sqrt[3]{c+d x}}{\sqrt{2}}\right)+2 \sqrt{b} \left(-8 i b^3 d^2 \sqrt[3]{c+d x} (e+f x)^2+4 b^2 f (c+d x)^{2/3} (-c f+8 d e+7 d f x)+2 i b f (19 c f+16 d e+35 d f x)-105 f^2 \sqrt[3]{c+d x}\right) \left(\cos \left(b (c+d x)^{2/3}\right)+i \sin \left(b (c+d x)^{2/3}\right)\right)\right)\right)}{64 b^{9/2} d^3}","\frac{3 \sqrt{\frac{\pi }{2}} \cos (a) (d e-c f)^2 C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[3]{c+d x}\right)}{2 b^{3/2} d^3}-\frac{3 \sqrt{\frac{\pi }{2}} \sin (a) (d e-c f)^2 S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[3]{c+d x}\right)}{2 b^{3/2} d^3}+\frac{315 \sqrt{\frac{\pi }{2}} f^2 \sin (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[3]{c+d x}\right)}{16 b^{9/2} d^3}+\frac{315 \sqrt{\frac{\pi }{2}} f^2 \cos (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[3]{c+d x}\right)}{16 b^{9/2} d^3}-\frac{315 f^2 \sqrt[3]{c+d x} \sin \left(a+b (c+d x)^{2/3}\right)}{16 b^4 d^3}+\frac{6 f (d e-c f) \cos \left(a+b (c+d x)^{2/3}\right)}{b^3 d^3}+\frac{105 f^2 (c+d x) \cos \left(a+b (c+d x)^{2/3}\right)}{8 b^3 d^3}+\frac{6 f (c+d x)^{2/3} (d e-c f) \sin \left(a+b (c+d x)^{2/3}\right)}{b^2 d^3}+\frac{21 f^2 (c+d x)^{5/3} \sin \left(a+b (c+d x)^{2/3}\right)}{4 b^2 d^3}-\frac{3 f (c+d x)^{4/3} (d e-c f) \cos \left(a+b (c+d x)^{2/3}\right)}{b d^3}-\frac{3 \sqrt[3]{c+d x} (d e-c f)^2 \cos \left(a+b (c+d x)^{2/3}\right)}{2 b d^3}-\frac{3 f^2 (c+d x)^{7/3} \cos \left(a+b (c+d x)^{2/3}\right)}{2 b d^3}",1,"(((-3*I)/64)*((Cos[a] + I*Sin[a])*((1 + I)*((-105*I)*f^2 + 8*b^3*(d*e - c*f)^2)*Sqrt[Pi/2]*Erfi[((1 + I)*Sqrt[b]*(c + d*x)^(1/3))/Sqrt[2]] + 2*Sqrt[b]*(-105*f^2*(c + d*x)^(1/3) - (8*I)*b^3*d^2*(c + d*x)^(1/3)*(e + f*x)^2 + 4*b^2*f*(c + d*x)^(2/3)*(8*d*e - c*f + 7*d*f*x) + (2*I)*b*f*(16*d*e + 19*c*f + 35*d*f*x))*(Cos[b*(c + d*x)^(2/3)] + I*Sin[b*(c + d*x)^(2/3)])) + (2*Sqrt[b]*(105*f^2*(c + d*x)^(1/3) - (8*I)*b^3*d^2*(c + d*x)^(1/3)*(e + f*x)^2 + 4*b^2*f*(c + d*x)^(2/3)*(-8*d*e + c*f - 7*d*f*x) + (2*I)*b*f*(16*d*e + 19*c*f + 35*d*f*x)) + (1 + I)*((105*I)*f^2 + 8*b^3*(d*e - c*f)^2)*Sqrt[Pi/2]*Erf[((1 + I)*Sqrt[b]*(c + d*x)^(1/3))/Sqrt[2]]*(Cos[b*(c + d*x)^(2/3)] + I*Sin[b*(c + d*x)^(2/3)]))*(Cos[a + b*(c + d*x)^(2/3)] - I*Sin[a + b*(c + d*x)^(2/3)])))/(b^(9/2)*d^3)","C",1
213,1,213,243,0.8524198,"\int (e+f x) \sin \left(a+b (c+d x)^{2/3}\right) \, dx","Integrate[(e + f*x)*Sin[a + b*(c + d*x)^(2/3)],x]","\frac{3 \left(\sqrt{2 \pi } b^{3/2} \cos (a) (d e-c f) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[3]{c+d x}\right)-\sqrt{2 \pi } b^{3/2} \sin (a) (d e-c f) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[3]{c+d x}\right)-2 b^2 d e \sqrt[3]{c+d x} \cos \left(a+b (c+d x)^{2/3}\right)-2 b^2 d f x \sqrt[3]{c+d x} \cos \left(a+b (c+d x)^{2/3}\right)+4 b f (c+d x)^{2/3} \sin \left(a+b (c+d x)^{2/3}\right)+4 f \cos \left(a+b (c+d x)^{2/3}\right)\right)}{4 b^3 d^2}","\frac{3 \sqrt{\frac{\pi }{2}} \cos (a) (d e-c f) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[3]{c+d x}\right)}{2 b^{3/2} d^2}-\frac{3 \sqrt{\frac{\pi }{2}} \sin (a) (d e-c f) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[3]{c+d x}\right)}{2 b^{3/2} d^2}+\frac{3 f \cos \left(a+b (c+d x)^{2/3}\right)}{b^3 d^2}+\frac{3 f (c+d x)^{2/3} \sin \left(a+b (c+d x)^{2/3}\right)}{b^2 d^2}-\frac{3 \sqrt[3]{c+d x} (d e-c f) \cos \left(a+b (c+d x)^{2/3}\right)}{2 b d^2}-\frac{3 f (c+d x)^{4/3} \cos \left(a+b (c+d x)^{2/3}\right)}{2 b d^2}",1,"(3*(4*f*Cos[a + b*(c + d*x)^(2/3)] - 2*b^2*d*e*(c + d*x)^(1/3)*Cos[a + b*(c + d*x)^(2/3)] - 2*b^2*d*f*x*(c + d*x)^(1/3)*Cos[a + b*(c + d*x)^(2/3)] + b^(3/2)*(d*e - c*f)*Sqrt[2*Pi]*Cos[a]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)^(1/3)] - b^(3/2)*(d*e - c*f)*Sqrt[2*Pi]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)^(1/3)]*Sin[a] + 4*b*f*(c + d*x)^(2/3)*Sin[a + b*(c + d*x)^(2/3)]))/(4*b^3*d^2)","A",1
214,1,114,130,0.1552449,"\int \sin \left(a+b (c+d x)^{2/3}\right) \, dx","Integrate[Sin[a + b*(c + d*x)^(2/3)],x]","-\frac{3 \left(-\sqrt{2 \pi } \cos (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[3]{c+d x}\right)+\sqrt{2 \pi } \sin (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[3]{c+d x}\right)+2 \sqrt{b} \sqrt[3]{c+d x} \cos \left(a+b (c+d x)^{2/3}\right)\right)}{4 b^{3/2} d}","\frac{3 \sqrt{\frac{\pi }{2}} \cos (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[3]{c+d x}\right)}{2 b^{3/2} d}-\frac{3 \sqrt{\frac{\pi }{2}} \sin (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[3]{c+d x}\right)}{2 b^{3/2} d}-\frac{3 \sqrt[3]{c+d x} \cos \left(a+b (c+d x)^{2/3}\right)}{2 b d}",1,"(-3*(2*Sqrt[b]*(c + d*x)^(1/3)*Cos[a + b*(c + d*x)^(2/3)] - Sqrt[2*Pi]*Cos[a]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)^(1/3)] + Sqrt[2*Pi]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)^(1/3)]*Sin[a]))/(4*b^(3/2)*d)","A",1
215,0,0,25,22.2999777,"\int \frac{\sin \left(a+b (c+d x)^{2/3}\right)}{e+f x} \, dx","Integrate[Sin[a + b*(c + d*x)^(2/3)]/(e + f*x),x]","\int \frac{\sin \left(a+b (c+d x)^{2/3}\right)}{e+f x} \, dx","\text{Int}\left(\frac{\sin \left(a+b (c+d x)^{2/3}\right)}{e+f x},x\right)",0,"Integrate[Sin[a + b*(c + d*x)^(2/3)]/(e + f*x), x]","A",-1
216,0,0,25,21.1021195,"\int \frac{\sin \left(a+b (c+d x)^{2/3}\right)}{(e+f x)^2} \, dx","Integrate[Sin[a + b*(c + d*x)^(2/3)]/(e + f*x)^2,x]","\int \frac{\sin \left(a+b (c+d x)^{2/3}\right)}{(e+f x)^2} \, dx","\text{Int}\left(\frac{\sin \left(a+b (c+d x)^{2/3}\right)}{(e+f x)^2},x\right)",0,"Integrate[Sin[a + b*(c + d*x)^(2/3)]/(e + f*x)^2, x]","A",-1
217,1,929,855,4.7194413,"\int (e+f x)^2 \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right) \, dx","Integrate[(e + f*x)^2*Sin[a + b/(c + d*x)^(1/3)],x]","-\frac{i \left((\cos (a)+i \sin (a)) \left(-i f^2 \text{Ei}\left(\frac{i b}{\sqrt[3]{c+d x}}\right) b^9-1008 c f^2 \text{Ei}\left(\frac{i b}{\sqrt[3]{c+d x}}\right) b^6+1008 d e f \text{Ei}\left(\frac{i b}{\sqrt[3]{c+d x}}\right) b^6+60480 i d^2 e^2 \text{Ei}\left(\frac{i b}{\sqrt[3]{c+d x}}\right) b^3+60480 i c^2 f^2 \text{Ei}\left(\frac{i b}{\sqrt[3]{c+d x}}\right) b^3-120960 i c d e f \text{Ei}\left(\frac{i b}{\sqrt[3]{c+d x}}\right) b^3+\sqrt[3]{c+d x} \left(f^2 b^8-i f^2 \sqrt[3]{c+d x} b^7-2 f^2 (c+d x)^{2/3} b^6+6 i f (168 d e-167 c f+d f x) b^5+24 f \sqrt[3]{c+d x} (42 d e-41 c f+d f x) b^4+24 i f (c+d x)^{2/3} (-84 d e+79 c f-5 d f x) b^3-144 \left(\left(420 e^2+42 f x e+5 f^2 x^2\right) d^2-2 c f (399 e+16 f x) d+383 c^2 f^2\right) b^2+1008 i \sqrt[3]{c+d x} \left(\left(60 e^2+24 f x e+5 f^2 x^2\right) d^2-2 c f (48 e+7 f x) d+41 c^2 f^2\right) b+40320 (c+d x)^{2/3} \left(\left(3 e^2+3 f x e+f^2 x^2\right) d^2-c f (3 e+f x) d+c^2 f^2\right)\right) \left(\cos \left(\frac{b}{\sqrt[3]{c+d x}}\right)+i \sin \left(\frac{b}{\sqrt[3]{c+d x}}\right)\right)\right)-\left(i \left(-60480 d^2 e^2+1008 \left(120 c-i b^3\right) d f e+\left(b^6+1008 i c b^3-60480 c^2\right) f^2\right) \text{Ei}\left(-\frac{i b}{\sqrt[3]{c+d x}}\right) \left(\cos \left(\frac{b}{\sqrt[3]{c+d x}}\right)+i \sin \left(\frac{b}{\sqrt[3]{c+d x}}\right)\right) b^3+\sqrt[3]{c+d x} \left(f^2 b^8+i f^2 \sqrt[3]{c+d x} b^7-2 f^2 (c+d x)^{2/3} b^6-6 i f (168 d e-167 c f+d f x) b^5+24 f \sqrt[3]{c+d x} (42 d e-41 c f+d f x) b^4+24 i f (c+d x)^{2/3} (84 d e-79 c f+5 d f x) b^3-144 \left(\left(420 e^2+42 f x e+5 f^2 x^2\right) d^2-2 c f (399 e+16 f x) d+383 c^2 f^2\right) b^2-1008 i \sqrt[3]{c+d x} \left(\left(60 e^2+24 f x e+5 f^2 x^2\right) d^2-2 c f (48 e+7 f x) d+41 c^2 f^2\right) b+40320 (c+d x)^{2/3} \left(\left(3 e^2+3 f x e+f^2 x^2\right) d^2-c f (3 e+f x) d+c^2 f^2\right)\right)\right) \left(\cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)-i \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)\right)\right)}{241920 d^3}","-\frac{f^2 \cos (a) \text{Ci}\left(\frac{b}{\sqrt[3]{c+d x}}\right) b^9}{120960 d^3}+\frac{f^2 \sin (a) \text{Si}\left(\frac{b}{\sqrt[3]{c+d x}}\right) b^9}{120960 d^3}+\frac{f^2 \sqrt[3]{c+d x} \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right) b^8}{120960 d^3}-\frac{f^2 (c+d x)^{2/3} \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right) b^7}{120960 d^3}+\frac{f (d e-c f) \text{Ci}\left(\frac{b}{\sqrt[3]{c+d x}}\right) \sin (a) b^6}{120 d^3}-\frac{f^2 (c+d x) \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right) b^6}{60480 d^3}+\frac{f (d e-c f) \cos (a) \text{Si}\left(\frac{b}{\sqrt[3]{c+d x}}\right) b^6}{120 d^3}+\frac{f^2 (c+d x)^{4/3} \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right) b^5}{20160 d^3}+\frac{f (d e-c f) \sqrt[3]{c+d x} \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right) b^5}{120 d^3}+\frac{f^2 (c+d x)^{5/3} \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right) b^4}{5040 d^3}+\frac{f (d e-c f) (c+d x)^{2/3} \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right) b^4}{120 d^3}-\frac{f^2 (c+d x)^2 \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right) b^3}{1008 d^3}-\frac{f (d e-c f) (c+d x) \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right) b^3}{60 d^3}+\frac{(d e-c f)^2 \cos (a) \text{Ci}\left(\frac{b}{\sqrt[3]{c+d x}}\right) b^3}{2 d^3}-\frac{(d e-c f)^2 \sin (a) \text{Si}\left(\frac{b}{\sqrt[3]{c+d x}}\right) b^3}{2 d^3}-\frac{f^2 (c+d x)^{7/3} \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right) b^2}{168 d^3}-\frac{f (d e-c f) (c+d x)^{4/3} \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right) b^2}{20 d^3}-\frac{(d e-c f)^2 \sqrt[3]{c+d x} \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right) b^2}{2 d^3}+\frac{f^2 (c+d x)^{8/3} \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right) b}{24 d^3}+\frac{f (d e-c f) (c+d x)^{5/3} \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right) b}{5 d^3}+\frac{(d e-c f)^2 (c+d x)^{2/3} \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right) b}{2 d^3}+\frac{f^2 (c+d x)^3 \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{3 d^3}+\frac{f (d e-c f) (c+d x)^2 \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{d^3}+\frac{(d e-c f)^2 (c+d x) \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{d^3}",1,"((-1/241920*I)*((Cos[a] + I*Sin[a])*((60480*I)*b^3*d^2*e^2*ExpIntegralEi[(I*b)/(c + d*x)^(1/3)] + 1008*b^6*d*e*f*ExpIntegralEi[(I*b)/(c + d*x)^(1/3)] - (120960*I)*b^3*c*d*e*f*ExpIntegralEi[(I*b)/(c + d*x)^(1/3)] - I*b^9*f^2*ExpIntegralEi[(I*b)/(c + d*x)^(1/3)] - 1008*b^6*c*f^2*ExpIntegralEi[(I*b)/(c + d*x)^(1/3)] + (60480*I)*b^3*c^2*f^2*ExpIntegralEi[(I*b)/(c + d*x)^(1/3)] + (c + d*x)^(1/3)*(b^8*f^2 - I*b^7*f^2*(c + d*x)^(1/3) - 2*b^6*f^2*(c + d*x)^(2/3) + (24*I)*b^3*f*(c + d*x)^(2/3)*(-84*d*e + 79*c*f - 5*d*f*x) + (6*I)*b^5*f*(168*d*e - 167*c*f + d*f*x) + 24*b^4*f*(c + d*x)^(1/3)*(42*d*e - 41*c*f + d*f*x) + 40320*(c + d*x)^(2/3)*(c^2*f^2 - c*d*f*(3*e + f*x) + d^2*(3*e^2 + 3*e*f*x + f^2*x^2)) + (1008*I)*b*(c + d*x)^(1/3)*(41*c^2*f^2 - 2*c*d*f*(48*e + 7*f*x) + d^2*(60*e^2 + 24*e*f*x + 5*f^2*x^2)) - 144*b^2*(383*c^2*f^2 - 2*c*d*f*(399*e + 16*f*x) + d^2*(420*e^2 + 42*e*f*x + 5*f^2*x^2)))*(Cos[b/(c + d*x)^(1/3)] + I*Sin[b/(c + d*x)^(1/3)])) - ((c + d*x)^(1/3)*(b^8*f^2 + I*b^7*f^2*(c + d*x)^(1/3) - 2*b^6*f^2*(c + d*x)^(2/3) - (6*I)*b^5*f*(168*d*e - 167*c*f + d*f*x) + 24*b^4*f*(c + d*x)^(1/3)*(42*d*e - 41*c*f + d*f*x) + (24*I)*b^3*f*(c + d*x)^(2/3)*(84*d*e - 79*c*f + 5*d*f*x) + 40320*(c + d*x)^(2/3)*(c^2*f^2 - c*d*f*(3*e + f*x) + d^2*(3*e^2 + 3*e*f*x + f^2*x^2)) - (1008*I)*b*(c + d*x)^(1/3)*(41*c^2*f^2 - 2*c*d*f*(48*e + 7*f*x) + d^2*(60*e^2 + 24*e*f*x + 5*f^2*x^2)) - 144*b^2*(383*c^2*f^2 - 2*c*d*f*(399*e + 16*f*x) + d^2*(420*e^2 + 42*e*f*x + 5*f^2*x^2))) + I*b^3*(-60480*d^2*e^2 + 1008*((-I)*b^3 + 120*c)*d*e*f + (b^6 + (1008*I)*b^3*c - 60480*c^2)*f^2)*ExpIntegralEi[((-I)*b)/(c + d*x)^(1/3)]*(Cos[b/(c + d*x)^(1/3)] + I*Sin[b/(c + d*x)^(1/3)]))*(Cos[a + b/(c + d*x)^(1/3)] - I*Sin[a + b/(c + d*x)^(1/3)])))/d^3","C",1
218,1,540,419,0.8910744,"\int (e+f x) \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right) \, dx","Integrate[(e + f*x)*Sin[a + b/(c + d*x)^(1/3)],x]","\frac{b^3 f \left(b^3 \sin (a) \text{Ci}\left(\frac{b}{\sqrt[3]{c+d x}}\right)+b^3 \cos (a) \text{Si}\left(\frac{b}{\sqrt[3]{c+d x}}\right)-120 c \cos (a) \text{Ci}\left(\frac{b}{\sqrt[3]{c+d x}}\right)+120 c \sin (a) \text{Si}\left(\frac{b}{\sqrt[3]{c+d x}}\right)\right)}{240 d^2}+\frac{b^3 e \left(\cos (a) \text{Ci}\left(\frac{b}{\sqrt[3]{c+d x}}\right)-\sin (a) \text{Si}\left(\frac{b}{\sqrt[3]{c+d x}}\right)\right)}{2 d}+\frac{e \sqrt[3]{c+d x} \cos \left(\frac{b}{\sqrt[3]{c+d x}}\right) \left(b^2 (-\sin (a))+b \cos (a) \sqrt[3]{c+d x}+2 \sin (a) (c+d x)^{2/3}\right)}{2 d}+\frac{e \sqrt[3]{c+d x} \sin \left(\frac{b}{\sqrt[3]{c+d x}}\right) \left(b^2 (-\cos (a))-b \sin (a) \sqrt[3]{c+d x}+2 \cos (a) (c+d x)^{2/3}\right)}{2 d}+\frac{f \sqrt[3]{c+d x} \cos \left(\frac{b}{\sqrt[3]{c+d x}}\right) \left(b^5 \cos (a)+b^4 \sin (a) \sqrt[3]{c+d x}-2 b^3 \cos (a) (c+d x)^{2/3}-6 b^2 \sin (a) (c+d x)+120 b^2 c \sin (a)+24 b \cos (a) (c+d x)^{4/3}-120 b c \cos (a) \sqrt[3]{c+d x}+120 \sin (a) (c+d x)^{5/3}-240 c \sin (a) (c+d x)^{2/3}\right)}{240 d^2}+\frac{f \sqrt[3]{c+d x} \sin \left(\frac{b}{\sqrt[3]{c+d x}}\right) \left(b^5 (-\sin (a))+b^4 \cos (a) \sqrt[3]{c+d x}+2 b^3 \sin (a) (c+d x)^{2/3}-6 b^2 \cos (a) (c+d x)+120 b^2 c \cos (a)-24 b \sin (a) (c+d x)^{4/3}+120 b c \sin (a) \sqrt[3]{c+d x}+120 \cos (a) (c+d x)^{5/3}-240 c \cos (a) (c+d x)^{2/3}\right)}{240 d^2}","\frac{b^6 f \sin (a) \text{Ci}\left(\frac{b}{\sqrt[3]{c+d x}}\right)}{240 d^2}+\frac{b^6 f \cos (a) \text{Si}\left(\frac{b}{\sqrt[3]{c+d x}}\right)}{240 d^2}+\frac{b^5 f \sqrt[3]{c+d x} \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{240 d^2}+\frac{b^4 f (c+d x)^{2/3} \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{240 d^2}+\frac{b^3 \cos (a) (d e-c f) \text{Ci}\left(\frac{b}{\sqrt[3]{c+d x}}\right)}{2 d^2}-\frac{b^3 \sin (a) (d e-c f) \text{Si}\left(\frac{b}{\sqrt[3]{c+d x}}\right)}{2 d^2}-\frac{b^3 f (c+d x) \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{120 d^2}-\frac{b^2 \sqrt[3]{c+d x} (d e-c f) \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{2 d^2}-\frac{b^2 f (c+d x)^{4/3} \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{40 d^2}+\frac{(c+d x) (d e-c f) \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{d^2}+\frac{b (c+d x)^{2/3} (d e-c f) \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{2 d^2}+\frac{f (c+d x)^2 \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{2 d^2}+\frac{b f (c+d x)^{5/3} \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{10 d^2}",1,"(e*(c + d*x)^(1/3)*Cos[b/(c + d*x)^(1/3)]*(b*(c + d*x)^(1/3)*Cos[a] - b^2*Sin[a] + 2*(c + d*x)^(2/3)*Sin[a]))/(2*d) + (f*(c + d*x)^(1/3)*Cos[b/(c + d*x)^(1/3)]*(b^5*Cos[a] - 120*b*c*(c + d*x)^(1/3)*Cos[a] - 2*b^3*(c + d*x)^(2/3)*Cos[a] + 24*b*(c + d*x)^(4/3)*Cos[a] + 120*b^2*c*Sin[a] + b^4*(c + d*x)^(1/3)*Sin[a] - 240*c*(c + d*x)^(2/3)*Sin[a] - 6*b^2*(c + d*x)*Sin[a] + 120*(c + d*x)^(5/3)*Sin[a]))/(240*d^2) + (e*(c + d*x)^(1/3)*(-(b^2*Cos[a]) + 2*(c + d*x)^(2/3)*Cos[a] - b*(c + d*x)^(1/3)*Sin[a])*Sin[b/(c + d*x)^(1/3)])/(2*d) + (f*(c + d*x)^(1/3)*(120*b^2*c*Cos[a] + b^4*(c + d*x)^(1/3)*Cos[a] - 240*c*(c + d*x)^(2/3)*Cos[a] - 6*b^2*(c + d*x)*Cos[a] + 120*(c + d*x)^(5/3)*Cos[a] - b^5*Sin[a] + 120*b*c*(c + d*x)^(1/3)*Sin[a] + 2*b^3*(c + d*x)^(2/3)*Sin[a] - 24*b*(c + d*x)^(4/3)*Sin[a])*Sin[b/(c + d*x)^(1/3)])/(240*d^2) + (b^3*e*(Cos[a]*CosIntegral[b/(c + d*x)^(1/3)] - Sin[a]*SinIntegral[b/(c + d*x)^(1/3)]))/(2*d) + (b^3*f*(-120*c*Cos[a]*CosIntegral[b/(c + d*x)^(1/3)] + b^3*CosIntegral[b/(c + d*x)^(1/3)]*Sin[a] + b^3*Cos[a]*SinIntegral[b/(c + d*x)^(1/3)] + 120*c*Sin[a]*SinIntegral[b/(c + d*x)^(1/3)]))/(240*d^2)","A",1
219,1,133,136,0.1109406,"\int \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right) \, dx","Integrate[Sin[a + b/(c + d*x)^(1/3)],x]","\frac{b^3 \cos (a) \text{Ci}\left(\frac{b}{\sqrt[3]{c+d x}}\right)-b^3 \sin (a) \text{Si}\left(\frac{b}{\sqrt[3]{c+d x}}\right)-b^2 \sqrt[3]{c+d x} \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)+2 c \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)+2 d x \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)+b (c+d x)^{2/3} \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{2 d}","\frac{b^3 \cos (a) \text{Ci}\left(\frac{b}{\sqrt[3]{c+d x}}\right)}{2 d}-\frac{b^3 \sin (a) \text{Si}\left(\frac{b}{\sqrt[3]{c+d x}}\right)}{2 d}-\frac{b^2 \sqrt[3]{c+d x} \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{2 d}+\frac{(c+d x) \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{d}+\frac{b (c+d x)^{2/3} \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{2 d}",1,"(b*(c + d*x)^(2/3)*Cos[a + b/(c + d*x)^(1/3)] + b^3*Cos[a]*CosIntegral[b/(c + d*x)^(1/3)] + 2*c*Sin[a + b/(c + d*x)^(1/3)] + 2*d*x*Sin[a + b/(c + d*x)^(1/3)] - b^2*(c + d*x)^(1/3)*Sin[a + b/(c + d*x)^(1/3)] - b^3*Sin[a]*SinIntegral[b/(c + d*x)^(1/3)])/(2*d)","A",1
220,1,170,434,2.8022874,"\int \frac{\sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{e+f x} \, dx","Integrate[Sin[a + b/(c + d*x)^(1/3)]/(e + f*x),x]","\frac{i \left((\cos (a)-i \sin (a)) \left(\text{RootSum}\left[\text{$\#$1}^3 f-c f+d e\&,e^{-\frac{i b}{\text{$\#$1}}} \text{Ei}\left(-i b \left(\frac{1}{\sqrt[3]{c+d x}}-\frac{1}{\text{$\#$1}}\right)\right)\&\right]-3 \text{Ei}\left(-\frac{i b}{\sqrt[3]{c+d x}}\right)\right)+(\cos (a)+i \sin (a)) \left(3 \text{Ei}\left(\frac{i b}{\sqrt[3]{c+d x}}\right)-\text{RootSum}\left[\text{$\#$1}^3 f-c f+d e\&,e^{\frac{i b}{\text{$\#$1}}} \text{Ei}\left(i b \left(\frac{1}{\sqrt[3]{c+d x}}-\frac{1}{\text{$\#$1}}\right)\right)\&\right]\right)\right)}{2 f}","\frac{\sin \left(a-\frac{b \sqrt[3]{f}}{\sqrt[3]{d e-c f}}\right) \text{Ci}\left(\frac{\sqrt[3]{f} b}{\sqrt[3]{d e-c f}}+\frac{b}{\sqrt[3]{c+d x}}\right)}{f}+\frac{\sin \left(a+\frac{\sqrt[3]{-1} b \sqrt[3]{f}}{\sqrt[3]{d e-c f}}\right) \text{Ci}\left(\frac{\sqrt[3]{-1} b \sqrt[3]{f}}{\sqrt[3]{d e-c f}}-\frac{b}{\sqrt[3]{c+d x}}\right)}{f}+\frac{\sin \left(a-\frac{(-1)^{2/3} b \sqrt[3]{f}}{\sqrt[3]{d e-c f}}\right) \text{Ci}\left(\frac{(-1)^{2/3} \sqrt[3]{f} b}{\sqrt[3]{d e-c f}}+\frac{b}{\sqrt[3]{c+d x}}\right)}{f}-\frac{3 \sin (a) \text{Ci}\left(\frac{b}{\sqrt[3]{c+d x}}\right)}{f}-\frac{\cos \left(a+\frac{\sqrt[3]{-1} b \sqrt[3]{f}}{\sqrt[3]{d e-c f}}\right) \text{Si}\left(\frac{\sqrt[3]{-1} b \sqrt[3]{f}}{\sqrt[3]{d e-c f}}-\frac{b}{\sqrt[3]{c+d x}}\right)}{f}+\frac{\cos \left(a-\frac{b \sqrt[3]{f}}{\sqrt[3]{d e-c f}}\right) \text{Si}\left(\frac{\sqrt[3]{f} b}{\sqrt[3]{d e-c f}}+\frac{b}{\sqrt[3]{c+d x}}\right)}{f}+\frac{\cos \left(a-\frac{(-1)^{2/3} b \sqrt[3]{f}}{\sqrt[3]{d e-c f}}\right) \text{Si}\left(\frac{(-1)^{2/3} \sqrt[3]{f} b}{\sqrt[3]{d e-c f}}+\frac{b}{\sqrt[3]{c+d x}}\right)}{f}-\frac{3 \cos (a) \text{Si}\left(\frac{b}{\sqrt[3]{c+d x}}\right)}{f}",1,"((I/2)*((-3*ExpIntegralEi[((-I)*b)/(c + d*x)^(1/3)] + RootSum[d*e - c*f + f*#1^3 & , ExpIntegralEi[(-I)*b*((c + d*x)^(-1/3) - #1^(-1))]/E^((I*b)/#1) & ])*(Cos[a] - I*Sin[a]) + (3*ExpIntegralEi[(I*b)/(c + d*x)^(1/3)] - RootSum[d*e - c*f + f*#1^3 & , E^((I*b)/#1)*ExpIntegralEi[I*b*((c + d*x)^(-1/3) - #1^(-1))] & ])*(Cos[a] + I*Sin[a])))/f","C",1
221,1,313,566,1.2724503,"\int \frac{\sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{(e+f x)^2} \, dx","Integrate[Sin[a + b/(c + d*x)^(1/3)]/(e + f*x)^2,x]","\frac{(\cos (a)+i \sin (a)) \left(b d (e+f x) \text{RootSum}\left[\text{$\#$1}^3 f-c f+d e\&,\frac{\text{Ei}\left(\frac{i b}{\sqrt[3]{c+d x}}\right)-e^{\frac{i b}{\text{$\#$1}}} \text{Ei}\left(i b \left(\frac{1}{\sqrt[3]{c+d x}}-\frac{1}{\text{$\#$1}}\right)\right)}{\text{$\#$1}}\&\right]+(c+d x) \left(-3 f \sin \left(\frac{b}{\sqrt[3]{c+d x}}\right)+3 i f \cos \left(\frac{b}{\sqrt[3]{c+d x}}\right)\right)\right)+i \left(\cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)-i \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)\right) \left(b d (e+f x) \left(\sin \left(\frac{b}{\sqrt[3]{c+d x}}\right)-i \cos \left(\frac{b}{\sqrt[3]{c+d x}}\right)\right) \text{RootSum}\left[\text{$\#$1}^3 f-c f+d e\&,\frac{\text{Ei}\left(-\frac{i b}{\sqrt[3]{c+d x}}\right)-e^{-\frac{i b}{\text{$\#$1}}} \text{Ei}\left(-i b \left(\frac{1}{\sqrt[3]{c+d x}}-\frac{1}{\text{$\#$1}}\right)\right)}{\text{$\#$1}}\&\right]-3 c f-3 d f x\right)}{6 f (e+f x) (c f-d e)}","-\frac{b d \cos \left(a+\frac{b \sqrt[3]{f}}{\sqrt[3]{c f-d e}}\right) \text{Ci}\left(\frac{b \sqrt[3]{f}}{\sqrt[3]{c f-d e}}-\frac{b}{\sqrt[3]{c+d x}}\right)}{3 f^{2/3} (c f-d e)^{4/3}}-\frac{(-1)^{2/3} b d \cos \left(a+\frac{(-1)^{2/3} b \sqrt[3]{f}}{\sqrt[3]{c f-d e}}\right) \text{Ci}\left(\frac{(-1)^{2/3} b \sqrt[3]{f}}{\sqrt[3]{c f-d e}}-\frac{b}{\sqrt[3]{c+d x}}\right)}{3 f^{2/3} (c f-d e)^{4/3}}+\frac{\sqrt[3]{-1} b d \cos \left(a-\frac{\sqrt[3]{-1} b \sqrt[3]{f}}{\sqrt[3]{c f-d e}}\right) \text{Ci}\left(\frac{\sqrt[3]{-1} \sqrt[3]{f} b}{\sqrt[3]{c f-d e}}+\frac{b}{\sqrt[3]{c+d x}}\right)}{3 f^{2/3} (c f-d e)^{4/3}}-\frac{b d \sin \left(a+\frac{b \sqrt[3]{f}}{\sqrt[3]{c f-d e}}\right) \text{Si}\left(\frac{b \sqrt[3]{f}}{\sqrt[3]{c f-d e}}-\frac{b}{\sqrt[3]{c+d x}}\right)}{3 f^{2/3} (c f-d e)^{4/3}}-\frac{(-1)^{2/3} b d \sin \left(a+\frac{(-1)^{2/3} b \sqrt[3]{f}}{\sqrt[3]{c f-d e}}\right) \text{Si}\left(\frac{(-1)^{2/3} b \sqrt[3]{f}}{\sqrt[3]{c f-d e}}-\frac{b}{\sqrt[3]{c+d x}}\right)}{3 f^{2/3} (c f-d e)^{4/3}}-\frac{\sqrt[3]{-1} b d \sin \left(a-\frac{\sqrt[3]{-1} b \sqrt[3]{f}}{\sqrt[3]{c f-d e}}\right) \text{Si}\left(\frac{\sqrt[3]{-1} \sqrt[3]{f} b}{\sqrt[3]{c f-d e}}+\frac{b}{\sqrt[3]{c+d x}}\right)}{3 f^{2/3} (c f-d e)^{4/3}}+\frac{(c+d x) \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{(e+f x) (d e-c f)}",1,"((Cos[a] + I*Sin[a])*(b*d*(e + f*x)*RootSum[d*e - c*f + f*#1^3 & , (ExpIntegralEi[(I*b)/(c + d*x)^(1/3)] - E^((I*b)/#1)*ExpIntegralEi[I*b*((c + d*x)^(-1/3) - #1^(-1))])/#1 & ] + (c + d*x)*((3*I)*f*Cos[b/(c + d*x)^(1/3)] - 3*f*Sin[b/(c + d*x)^(1/3)])) + I*(-3*c*f - 3*d*f*x + b*d*(e + f*x)*RootSum[d*e - c*f + f*#1^3 & , (ExpIntegralEi[((-I)*b)/(c + d*x)^(1/3)] - ExpIntegralEi[(-I)*b*((c + d*x)^(-1/3) - #1^(-1))]/E^((I*b)/#1))/#1 & ]*((-I)*Cos[b/(c + d*x)^(1/3)] + Sin[b/(c + d*x)^(1/3)]))*(Cos[a + b/(c + d*x)^(1/3)] - I*Sin[a + b/(c + d*x)^(1/3)]))/(6*f*(-(d*e) + c*f)*(e + f*x))","C",1
222,1,613,630,3.1015054,"\int (e+f x)^2 \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right) \, dx","Integrate[(e + f*x)^2*Sin[a + b/(c + d*x)^(2/3)],x]","\frac{i e^{-i a} \left(315 i e^{2 i a} b^3 f (c f-d e) \text{Ei}\left(\frac{i b}{(c+d x)^{2/3}}\right)+4 \sqrt[4]{-1} \sqrt{\pi } e^{2 i a} b^{3/2} \left(f^2 \left(8 b^3+315 i c^2\right)-630 i c d e f+315 i d^2 e^2\right) \text{erfi}\left(\frac{\sqrt[4]{-1} \sqrt{b}}{\sqrt[3]{c+d x}}\right)-\sqrt[3]{c+d x} e^{i \left(2 a+\frac{b}{(c+d x)^{2/3}}\right)} \left(32 b^4 f^2-16 i b^3 f^2 (c+d x)^{2/3}+3 b^2 f \sqrt[3]{c+d x} (97 c f-105 d e-8 d f x)+15 i b \left(f^2 \left(67 c^2-13 c d x+4 d^2 x^2\right)+21 d e f (d x-7 c)+84 d^2 e^2\right)+210 (c+d x)^{2/3} \left(c^2 f^2-c d f (3 e+f x)+d^2 \left(3 e^2+3 e f x+f^2 x^2\right)\right)\right)+315 i b^3 f (c f-d e) \text{Ei}\left(-\frac{i b}{(c+d x)^{2/3}}\right)-4 \sqrt[4]{-1} \sqrt{\pi } b^{3/2} \left(f^2 \left(315 c^2+8 i b^3\right)-630 c d e f+315 d^2 e^2\right) \text{erfi}\left(\frac{(-1)^{3/4} \sqrt{b}}{\sqrt[3]{c+d x}}\right)+\sqrt[3]{c+d x} e^{-\frac{i b}{(c+d x)^{2/3}}} \left(32 b^4 f^2+16 i b^3 f^2 (c+d x)^{2/3}+3 b^2 f \sqrt[3]{c+d x} (97 c f-105 d e-8 d f x)-15 i b \left(f^2 \left(67 c^2-13 c d x+4 d^2 x^2\right)+21 d e f (d x-7 c)+84 d^2 e^2\right)+210 (c+d x)^{2/3} \left(c^2 f^2-c d f (3 e+f x)+d^2 \left(3 e^2+3 e f x+f^2 x^2\right)\right)\right)\right)}{1260 d^3}","\frac{2 \sqrt{2 \pi } b^{3/2} \sin (a) (d e-c f)^2 C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)}{d^3}+\frac{2 \sqrt{2 \pi } b^{3/2} \cos (a) (d e-c f)^2 S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)}{d^3}-\frac{16 \sqrt{2 \pi } b^{9/2} f^2 \cos (a) C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)}{315 d^3}+\frac{16 \sqrt{2 \pi } b^{9/2} f^2 \sin (a) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)}{315 d^3}+\frac{16 b^4 f^2 \sqrt[3]{c+d x} \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{315 d^3}+\frac{b^3 f \cos (a) (d e-c f) \text{Ci}\left(\frac{b}{(c+d x)^{2/3}}\right)}{2 d^3}-\frac{b^3 f \sin (a) (d e-c f) \text{Si}\left(\frac{b}{(c+d x)^{2/3}}\right)}{2 d^3}-\frac{8 b^3 f^2 (c+d x) \cos \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{315 d^3}-\frac{b^2 f (c+d x)^{2/3} (d e-c f) \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{2 d^3}-\frac{4 b^2 f^2 (c+d x)^{5/3} \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{105 d^3}+\frac{f (c+d x)^2 (d e-c f) \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{d^3}+\frac{(c+d x) (d e-c f)^2 \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{d^3}+\frac{b f (c+d x)^{4/3} (d e-c f) \cos \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{2 d^3}+\frac{2 b \sqrt[3]{c+d x} (d e-c f)^2 \cos \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{d^3}+\frac{f^2 (c+d x)^3 \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{3 d^3}+\frac{2 b f^2 (c+d x)^{7/3} \cos \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{21 d^3}",1,"((I/1260)*(((c + d*x)^(1/3)*(32*b^4*f^2 + (16*I)*b^3*f^2*(c + d*x)^(2/3) + 3*b^2*f*(c + d*x)^(1/3)*(-105*d*e + 97*c*f - 8*d*f*x) - (15*I)*b*(84*d^2*e^2 + 21*d*e*f*(-7*c + d*x) + f^2*(67*c^2 - 13*c*d*x + 4*d^2*x^2)) + 210*(c + d*x)^(2/3)*(c^2*f^2 - c*d*f*(3*e + f*x) + d^2*(3*e^2 + 3*e*f*x + f^2*x^2))))/E^((I*b)/(c + d*x)^(2/3)) - E^(I*(2*a + b/(c + d*x)^(2/3)))*(c + d*x)^(1/3)*(32*b^4*f^2 - (16*I)*b^3*f^2*(c + d*x)^(2/3) + 3*b^2*f*(c + d*x)^(1/3)*(-105*d*e + 97*c*f - 8*d*f*x) + (15*I)*b*(84*d^2*e^2 + 21*d*e*f*(-7*c + d*x) + f^2*(67*c^2 - 13*c*d*x + 4*d^2*x^2)) + 210*(c + d*x)^(2/3)*(c^2*f^2 - c*d*f*(3*e + f*x) + d^2*(3*e^2 + 3*e*f*x + f^2*x^2))) + 4*(-1)^(1/4)*b^(3/2)*E^((2*I)*a)*((315*I)*d^2*e^2 - (630*I)*c*d*e*f + (8*b^3 + (315*I)*c^2)*f^2)*Sqrt[Pi]*Erfi[((-1)^(1/4)*Sqrt[b])/(c + d*x)^(1/3)] - 4*(-1)^(1/4)*b^(3/2)*(315*d^2*e^2 - 630*c*d*e*f + ((8*I)*b^3 + 315*c^2)*f^2)*Sqrt[Pi]*Erfi[((-1)^(3/4)*Sqrt[b])/(c + d*x)^(1/3)] + (315*I)*b^3*f*(-(d*e) + c*f)*ExpIntegralEi[((-I)*b)/(c + d*x)^(2/3)] + (315*I)*b^3*E^((2*I)*a)*f*(-(d*e) + c*f)*ExpIntegralEi[(I*b)/(c + d*x)^(2/3)]))/(d^3*E^(I*a))","C",1
223,1,378,318,1.1846626,"\int (e+f x) \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right) \, dx","Integrate[(e + f*x)*Sin[a + b/(c + d*x)^(2/3)],x]","\frac{8 \sqrt{2 \pi } b^{3/2} \cos (a) (d e-c f) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)+8 \sqrt{2 \pi } b^{3/2} d e \sin (a) C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)-8 \sqrt{2 \pi } b^{3/2} c f \sin (a) C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)+b^3 f \cos (a) \text{Ci}\left(\frac{b}{(c+d x)^{2/3}}\right)-b^3 f \sin (a) \text{Si}\left(\frac{b}{(c+d x)^{2/3}}\right)-b^2 f (c+d x)^{2/3} \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)-2 c^2 f \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)+4 d^2 e x \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)+2 d^2 f x^2 \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)+4 c d e \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)+8 b d e \sqrt[3]{c+d x} \cos \left(a+\frac{b}{(c+d x)^{2/3}}\right)-7 b c f \sqrt[3]{c+d x} \cos \left(a+\frac{b}{(c+d x)^{2/3}}\right)+b d f x \sqrt[3]{c+d x} \cos \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{4 d^2}","\frac{2 \sqrt{2 \pi } b^{3/2} \sin (a) (d e-c f) C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)}{d^2}+\frac{2 \sqrt{2 \pi } b^{3/2} \cos (a) (d e-c f) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)}{d^2}+\frac{b^3 f \cos (a) \text{Ci}\left(\frac{b}{(c+d x)^{2/3}}\right)}{4 d^2}-\frac{b^3 f \sin (a) \text{Si}\left(\frac{b}{(c+d x)^{2/3}}\right)}{4 d^2}-\frac{b^2 f (c+d x)^{2/3} \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{4 d^2}+\frac{(c+d x) (d e-c f) \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{d^2}+\frac{2 b \sqrt[3]{c+d x} (d e-c f) \cos \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{d^2}+\frac{f (c+d x)^2 \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{2 d^2}+\frac{b f (c+d x)^{4/3} \cos \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{4 d^2}",1,"(8*b*d*e*(c + d*x)^(1/3)*Cos[a + b/(c + d*x)^(2/3)] - 7*b*c*f*(c + d*x)^(1/3)*Cos[a + b/(c + d*x)^(2/3)] + b*d*f*x*(c + d*x)^(1/3)*Cos[a + b/(c + d*x)^(2/3)] + b^3*f*Cos[a]*CosIntegral[b/(c + d*x)^(2/3)] + 8*b^(3/2)*(d*e - c*f)*Sqrt[2*Pi]*Cos[a]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)^(1/3)] + 8*b^(3/2)*d*e*Sqrt[2*Pi]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)^(1/3)]*Sin[a] - 8*b^(3/2)*c*f*Sqrt[2*Pi]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)^(1/3)]*Sin[a] + 4*c*d*e*Sin[a + b/(c + d*x)^(2/3)] - 2*c^2*f*Sin[a + b/(c + d*x)^(2/3)] + 4*d^2*e*x*Sin[a + b/(c + d*x)^(2/3)] + 2*d^2*f*x^2*Sin[a + b/(c + d*x)^(2/3)] - b^2*f*(c + d*x)^(2/3)*Sin[a + b/(c + d*x)^(2/3)] - b^3*f*Sin[a]*SinIntegral[b/(c + d*x)^(2/3)])/(4*d^2)","A",1
224,1,146,141,0.1585604,"\int \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right) \, dx","Integrate[Sin[a + b/(c + d*x)^(2/3)],x]","\frac{2 \sqrt{2 \pi } b^{3/2} \sin (a) C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)+2 \sqrt{2 \pi } b^{3/2} \cos (a) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)+c \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)+d x \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)+2 b \sqrt[3]{c+d x} \cos \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{d}","\frac{2 \sqrt{2 \pi } b^{3/2} \sin (a) C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)}{d}+\frac{2 \sqrt{2 \pi } b^{3/2} \cos (a) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)}{d}+\frac{(c+d x) \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{d}+\frac{2 b \sqrt[3]{c+d x} \cos \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{d}",1,"(2*b*(c + d*x)^(1/3)*Cos[a + b/(c + d*x)^(2/3)] + 2*b^(3/2)*Sqrt[2*Pi]*Cos[a]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)^(1/3)] + 2*b^(3/2)*Sqrt[2*Pi]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)^(1/3)]*Sin[a] + c*Sin[a + b/(c + d*x)^(2/3)] + d*x*Sin[a + b/(c + d*x)^(2/3)])/d","A",1
225,0,0,25,30.1589802,"\int \frac{\sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{e+f x} \, dx","Integrate[Sin[a + b/(c + d*x)^(2/3)]/(e + f*x),x]","\int \frac{\sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{e+f x} \, dx","\text{Int}\left(\frac{\sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{e+f x},x\right)",0,"Integrate[Sin[a + b/(c + d*x)^(2/3)]/(e + f*x), x]","A",-1
226,-1,0,25,180.0328979,"\int \frac{\sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{(e+f x)^2} \, dx","Integrate[Sin[a + b/(c + d*x)^(2/3)]/(e + f*x)^2,x]","\text{\$Aborted}","\text{Int}\left(\frac{\sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{(e+f x)^2},x\right)",0,"$Aborted","F",-1
227,1,226,289,0.5653658,"\int (c e+d e x)^{4/3} \sin \left(a+b \sqrt[3]{c+d x}\right) \, dx","Integrate[(c*e + d*e*x)^(4/3)*Sin[a + b*(c + d*x)^(1/3)],x]","\frac{3 (e (c+d x))^{4/3} \left(\sin \left(b \sqrt[3]{c+d x}\right) \left(6 b \cos (a) \left(b^4 (c+d x)^{5/3}-20 b^2 (c+d x)+120 \sqrt[3]{c+d x}\right)+\sin (a) \left(b^6 (c+d x)^2-30 b^4 (c+d x)^{4/3}+360 b^2 (c+d x)^{2/3}-720\right)\right)-\cos \left(b \sqrt[3]{c+d x}\right) \left(\cos (a) \left(b^6 (c+d x)^2-30 b^4 (c+d x)^{4/3}+360 b^2 (c+d x)^{2/3}-720\right)-6 b \sin (a) \left(b^4 (c+d x)^{5/3}-20 b^2 (c+d x)+120 \sqrt[3]{c+d x}\right)\right)\right)}{b^7 d (c+d x)^{4/3}}","\frac{2160 e \sqrt[3]{e (c+d x)} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^7 d \sqrt[3]{c+d x}}+\frac{2160 e \sqrt[3]{e (c+d x)} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^6 d}-\frac{1080 e \sqrt[3]{c+d x} \sqrt[3]{e (c+d x)} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^5 d}-\frac{360 e (c+d x)^{2/3} \sqrt[3]{e (c+d x)} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^4 d}+\frac{90 e (c+d x) \sqrt[3]{e (c+d x)} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d}+\frac{18 e (c+d x)^{4/3} \sqrt[3]{e (c+d x)} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d}-\frac{3 e (c+d x)^{5/3} \sqrt[3]{e (c+d x)} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b d}",1,"(3*(e*(c + d*x))^(4/3)*(-(Cos[b*(c + d*x)^(1/3)]*((-720 + 360*b^2*(c + d*x)^(2/3) - 30*b^4*(c + d*x)^(4/3) + b^6*(c + d*x)^2)*Cos[a] - 6*b*(120*(c + d*x)^(1/3) - 20*b^2*(c + d*x) + b^4*(c + d*x)^(5/3))*Sin[a])) + (6*b*(120*(c + d*x)^(1/3) - 20*b^2*(c + d*x) + b^4*(c + d*x)^(5/3))*Cos[a] + (-720 + 360*b^2*(c + d*x)^(2/3) - 30*b^4*(c + d*x)^(4/3) + b^6*(c + d*x)^2)*Sin[a])*Sin[b*(c + d*x)^(1/3)]))/(b^7*d*(c + d*x)^(4/3))","A",1
228,1,111,202,0.2955925,"\int (c e+d e x)^{2/3} \sin \left(a+b \sqrt[3]{c+d x}\right) \, dx","Integrate[(c*e + d*e*x)^(2/3)*Sin[a + b*(c + d*x)^(1/3)],x]","-\frac{3 (e (c+d x))^{2/3} \left(\left(b^4 (c+d x)^{4/3}-12 b^2 (c+d x)^{2/3}+24\right) \cos \left(a+b \sqrt[3]{c+d x}\right)-4 b \left(b^2 (c+d x)-6 \sqrt[3]{c+d x}\right) \sin \left(a+b \sqrt[3]{c+d x}\right)\right)}{b^5 d (c+d x)^{2/3}}","-\frac{72 (e (c+d x))^{2/3} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^5 d (c+d x)^{2/3}}-\frac{72 (e (c+d x))^{2/3} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^4 d \sqrt[3]{c+d x}}+\frac{36 (e (c+d x))^{2/3} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d}+\frac{12 \sqrt[3]{c+d x} (e (c+d x))^{2/3} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d}-\frac{3 (c+d x)^{2/3} (e (c+d x))^{2/3} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b d}",1,"(-3*(e*(c + d*x))^(2/3)*((24 - 12*b^2*(c + d*x)^(2/3) + b^4*(c + d*x)^(4/3))*Cos[a + b*(c + d*x)^(1/3)] - 4*b*(-6*(c + d*x)^(1/3) + b^2*(c + d*x))*Sin[a + b*(c + d*x)^(1/3)]))/(b^5*d*(c + d*x)^(2/3))","A",1
229,1,97,160,0.2244402,"\int \sqrt[3]{c e+d e x} \sin \left(a+b \sqrt[3]{c+d x}\right) \, dx","Integrate[(c*e + d*e*x)^(1/3)*Sin[a + b*(c + d*x)^(1/3)],x]","-\frac{3 \sqrt[3]{e (c+d x)} \left(\left(b^3 (c+d x)-6 b \sqrt[3]{c+d x}\right) \cos \left(a+b \sqrt[3]{c+d x}\right)-3 \left(b^2 (c+d x)^{2/3}-2\right) \sin \left(a+b \sqrt[3]{c+d x}\right)\right)}{b^4 d \sqrt[3]{c+d x}}","-\frac{18 \sqrt[3]{e (c+d x)} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^4 d \sqrt[3]{c+d x}}+\frac{18 \sqrt[3]{e (c+d x)} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d}+\frac{9 \sqrt[3]{c+d x} \sqrt[3]{e (c+d x)} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d}-\frac{3 (c+d x)^{2/3} \sqrt[3]{e (c+d x)} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b d}",1,"(-3*(e*(c + d*x))^(1/3)*((-6*b*(c + d*x)^(1/3) + b^3*(c + d*x))*Cos[a + b*(c + d*x)^(1/3)] - 3*(-2 + b^2*(c + d*x)^(2/3))*Sin[a + b*(c + d*x)^(1/3)]))/(b^4*d*(c + d*x)^(1/3))","A",1
230,1,70,85,0.0781456,"\int \frac{\sin \left(a+b \sqrt[3]{c+d x}\right)}{\sqrt[3]{c e+d e x}} \, dx","Integrate[Sin[a + b*(c + d*x)^(1/3)]/(c*e + d*e*x)^(1/3),x]","\frac{3 \sqrt[3]{c+d x} \sin \left(a+b \sqrt[3]{c+d x}\right)-3 b (c+d x)^{2/3} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d \sqrt[3]{e (c+d x)}}","\frac{3 \sqrt[3]{c+d x} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d \sqrt[3]{e (c+d x)}}-\frac{3 (c+d x)^{2/3} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b d \sqrt[3]{e (c+d x)}}",1,"(-3*b*(c + d*x)^(2/3)*Cos[a + b*(c + d*x)^(1/3)] + 3*(c + d*x)^(1/3)*Sin[a + b*(c + d*x)^(1/3)])/(b^2*d*(e*(c + d*x))^(1/3))","A",1
231,1,42,42,0.0686423,"\int \frac{\sin \left(a+b \sqrt[3]{c+d x}\right)}{(c e+d e x)^{2/3}} \, dx","Integrate[Sin[a + b*(c + d*x)^(1/3)]/(c*e + d*e*x)^(2/3),x]","-\frac{3 (c+d x)^{2/3} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b d (e (c+d x))^{2/3}}","-\frac{3 (c+d x)^{2/3} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b d (e (c+d x))^{2/3}}",1,"(-3*(c + d*x)^(2/3)*Cos[a + b*(c + d*x)^(1/3)])/(b*d*(e*(c + d*x))^(2/3))","A",1
232,1,85,120,0.1554917,"\int \frac{\sin \left(a+b \sqrt[3]{c+d x}\right)}{(c e+d e x)^{4/3}} \, dx","Integrate[Sin[a + b*(c + d*x)^(1/3)]/(c*e + d*e*x)^(4/3),x]","-\frac{3 \left(-b \cos (a) \sqrt[3]{c+d x} \text{Ci}\left(b \sqrt[3]{c+d x}\right)+b \sin (a) \sqrt[3]{c+d x} \text{Si}\left(b \sqrt[3]{c+d x}\right)+\sin \left(a+b \sqrt[3]{c+d x}\right)\right)}{d e \sqrt[3]{e (c+d x)}}","\frac{3 b \cos (a) \sqrt[3]{c+d x} \text{Ci}\left(b \sqrt[3]{c+d x}\right)}{d e \sqrt[3]{e (c+d x)}}-\frac{3 b \sin (a) \sqrt[3]{c+d x} \text{Si}\left(b \sqrt[3]{c+d x}\right)}{d e \sqrt[3]{e (c+d x)}}-\frac{3 \sin \left(a+b \sqrt[3]{c+d x}\right)}{d e \sqrt[3]{e (c+d x)}}",1,"(-3*(-(b*(c + d*x)^(1/3)*Cos[a]*CosIntegral[b*(c + d*x)^(1/3)]) + Sin[a + b*(c + d*x)^(1/3)] + b*(c + d*x)^(1/3)*Sin[a]*SinIntegral[b*(c + d*x)^(1/3)]))/(d*e*(e*(c + d*x))^(1/3))","A",1
233,1,115,175,0.1985072,"\int \frac{\sin \left(a+b \sqrt[3]{c+d x}\right)}{(c e+d e x)^{5/3}} \, dx","Integrate[Sin[a + b*(c + d*x)^(1/3)]/(c*e + d*e*x)^(5/3),x]","-\frac{3 \left(b^2 \sin (a) (c+d x)^{2/3} \text{Ci}\left(b \sqrt[3]{c+d x}\right)+b^2 \cos (a) (c+d x)^{2/3} \text{Si}\left(b \sqrt[3]{c+d x}\right)+\sin \left(a+b \sqrt[3]{c+d x}\right)+b \sqrt[3]{c+d x} \cos \left(a+b \sqrt[3]{c+d x}\right)\right)}{2 d e (e (c+d x))^{2/3}}","-\frac{3 b^2 \sin (a) (c+d x)^{2/3} \text{Ci}\left(b \sqrt[3]{c+d x}\right)}{2 d e (e (c+d x))^{2/3}}-\frac{3 b^2 \cos (a) (c+d x)^{2/3} \text{Si}\left(b \sqrt[3]{c+d x}\right)}{2 d e (e (c+d x))^{2/3}}-\frac{3 \sin \left(a+b \sqrt[3]{c+d x}\right)}{2 d e (e (c+d x))^{2/3}}-\frac{3 b \sqrt[3]{c+d x} \cos \left(a+b \sqrt[3]{c+d x}\right)}{2 d e (e (c+d x))^{2/3}}",1,"(-3*(b*(c + d*x)^(1/3)*Cos[a + b*(c + d*x)^(1/3)] + b^2*(c + d*x)^(2/3)*CosIntegral[b*(c + d*x)^(1/3)]*Sin[a] + Sin[a + b*(c + d*x)^(1/3)] + b^2*(c + d*x)^(2/3)*Cos[a]*SinIntegral[b*(c + d*x)^(1/3)]))/(2*d*e*(e*(c + d*x))^(2/3))","A",1
234,1,184,267,0.3767341,"\int \frac{\sin \left(a+b \sqrt[3]{c+d x}\right)}{(c e+d e x)^{7/3}} \, dx","Integrate[Sin[a + b*(c + d*x)^(1/3)]/(c*e + d*e*x)^(7/3),x]","\frac{b^4 \sin (a) (c+d x)^{4/3} \text{Ci}\left(b \sqrt[3]{c+d x}\right)+b^4 \cos (a) (c+d x)^{4/3} \text{Si}\left(b \sqrt[3]{c+d x}\right)+b^3 c \cos \left(a+b \sqrt[3]{c+d x}\right)+b^3 d x \cos \left(a+b \sqrt[3]{c+d x}\right)+b^2 (c+d x)^{2/3} \sin \left(a+b \sqrt[3]{c+d x}\right)-6 \sin \left(a+b \sqrt[3]{c+d x}\right)-2 b \sqrt[3]{c+d x} \cos \left(a+b \sqrt[3]{c+d x}\right)}{8 d e (e (c+d x))^{4/3}}","\frac{b^4 \sin (a) \sqrt[3]{c+d x} \text{Ci}\left(b \sqrt[3]{c+d x}\right)}{8 d e^2 \sqrt[3]{e (c+d x)}}+\frac{b^4 \cos (a) \sqrt[3]{c+d x} \text{Si}\left(b \sqrt[3]{c+d x}\right)}{8 d e^2 \sqrt[3]{e (c+d x)}}+\frac{b^3 \cos \left(a+b \sqrt[3]{c+d x}\right)}{8 d e^2 \sqrt[3]{e (c+d x)}}+\frac{b^2 \sin \left(a+b \sqrt[3]{c+d x}\right)}{8 d e^2 \sqrt[3]{c+d x} \sqrt[3]{e (c+d x)}}-\frac{3 \sin \left(a+b \sqrt[3]{c+d x}\right)}{4 d e^2 (c+d x) \sqrt[3]{e (c+d x)}}-\frac{b \cos \left(a+b \sqrt[3]{c+d x}\right)}{4 d e^2 (c+d x)^{2/3} \sqrt[3]{e (c+d x)}}",1,"(b^3*c*Cos[a + b*(c + d*x)^(1/3)] + b^3*d*x*Cos[a + b*(c + d*x)^(1/3)] - 2*b*(c + d*x)^(1/3)*Cos[a + b*(c + d*x)^(1/3)] + b^4*(c + d*x)^(4/3)*CosIntegral[b*(c + d*x)^(1/3)]*Sin[a] - 6*Sin[a + b*(c + d*x)^(1/3)] + b^2*(c + d*x)^(2/3)*Sin[a + b*(c + d*x)^(1/3)] + b^4*(c + d*x)^(4/3)*Cos[a]*SinIntegral[b*(c + d*x)^(1/3)])/(8*d*e*(e*(c + d*x))^(4/3))","A",1
235,1,175,267,0.7573298,"\int (c e+d e x)^{4/3} \sin \left(a+b (c+d x)^{2/3}\right) \, dx","Integrate[(c*e + d*e*x)^(4/3)*Sin[a + b*(c + d*x)^(2/3)],x]","-\frac{3 (e (c+d x))^{4/3} \left(2 \sqrt{b} \left(\sqrt[3]{c+d x} \left(4 b^2 (c+d x)^{4/3}-15\right) \cos \left(a+b (c+d x)^{2/3}\right)-10 b (c+d x) \sin \left(a+b (c+d x)^{2/3}\right)\right)+15 \sqrt{2 \pi } \cos (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[3]{c+d x}\right)-15 \sqrt{2 \pi } \sin (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[3]{c+d x}\right)\right)}{16 b^{7/2} d (c+d x)^{4/3}}","-\frac{45 \sqrt{\pi } e \cos (a) \sqrt[3]{e (c+d x)} C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[3]{c+d x}\right)}{8 \sqrt{2} b^{7/2} d \sqrt[3]{c+d x}}+\frac{45 \sqrt{\pi } e \sin (a) \sqrt[3]{e (c+d x)} S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[3]{c+d x}\right)}{8 \sqrt{2} b^{7/2} d \sqrt[3]{c+d x}}+\frac{45 e \sqrt[3]{e (c+d x)} \cos \left(a+b (c+d x)^{2/3}\right)}{8 b^3 d}+\frac{15 e (c+d x)^{2/3} \sqrt[3]{e (c+d x)} \sin \left(a+b (c+d x)^{2/3}\right)}{4 b^2 d}-\frac{3 e (c+d x)^{4/3} \sqrt[3]{e (c+d x)} \cos \left(a+b (c+d x)^{2/3}\right)}{2 b d}",1,"(-3*(e*(c + d*x))^(4/3)*(15*Sqrt[2*Pi]*Cos[a]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)^(1/3)] - 15*Sqrt[2*Pi]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)^(1/3)]*Sin[a] + 2*Sqrt[b]*((c + d*x)^(1/3)*(-15 + 4*b^2*(c + d*x)^(4/3))*Cos[a + b*(c + d*x)^(2/3)] - 10*b*(c + d*x)*Sin[a + b*(c + d*x)^(2/3)])))/(16*b^(7/2)*d*(c + d*x)^(4/3))","A",1
236,1,160,227,0.465314,"\int (c e+d e x)^{2/3} \sin \left(a+b (c+d x)^{2/3}\right) \, dx","Integrate[(c*e + d*e*x)^(2/3)*Sin[a + b*(c + d*x)^(2/3)],x]","-\frac{3 (e (c+d x))^{2/3} \left(3 \sqrt{2 \pi } \sin (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[3]{c+d x}\right)+3 \sqrt{2 \pi } \cos (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[3]{c+d x}\right)+2 \sqrt{b} \left(2 b (c+d x) \cos \left(a+b (c+d x)^{2/3}\right)-3 \sqrt[3]{c+d x} \sin \left(a+b (c+d x)^{2/3}\right)\right)\right)}{8 b^{5/2} d (c+d x)^{2/3}}","-\frac{9 \sqrt{\pi } \sin (a) (e (c+d x))^{2/3} C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[3]{c+d x}\right)}{4 \sqrt{2} b^{5/2} d (c+d x)^{2/3}}-\frac{9 \sqrt{\pi } \cos (a) (e (c+d x))^{2/3} S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[3]{c+d x}\right)}{4 \sqrt{2} b^{5/2} d (c+d x)^{2/3}}+\frac{9 (e (c+d x))^{2/3} \sin \left(a+b (c+d x)^{2/3}\right)}{4 b^2 d \sqrt[3]{c+d x}}-\frac{3 \sqrt[3]{c+d x} (e (c+d x))^{2/3} \cos \left(a+b (c+d x)^{2/3}\right)}{2 b d}",1,"(-3*(e*(c + d*x))^(2/3)*(3*Sqrt[2*Pi]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)^(1/3)] + 3*Sqrt[2*Pi]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)^(1/3)]*Sin[a] + 2*Sqrt[b]*(2*b*(c + d*x)*Cos[a + b*(c + d*x)^(2/3)] - 3*(c + d*x)^(1/3)*Sin[a + b*(c + d*x)^(2/3)])))/(8*b^(5/2)*d*(c + d*x)^(2/3))","A",1
237,1,72,89,0.0599493,"\int \sqrt[3]{c e+d e x} \sin \left(a+b (c+d x)^{2/3}\right) \, dx","Integrate[(c*e + d*e*x)^(1/3)*Sin[a + b*(c + d*x)^(2/3)],x]","-\frac{3 \sqrt[3]{e (c+d x)} \left(b (c+d x)^{2/3} \cos \left(a+b (c+d x)^{2/3}\right)-\sin \left(a+b (c+d x)^{2/3}\right)\right)}{2 b^2 d \sqrt[3]{c+d x}}","\frac{3 \sqrt[3]{e (c+d x)} \sin \left(a+b (c+d x)^{2/3}\right)}{2 b^2 d \sqrt[3]{c+d x}}-\frac{3 \sqrt[3]{c+d x} \sqrt[3]{e (c+d x)} \cos \left(a+b (c+d x)^{2/3}\right)}{2 b d}",1,"(-3*(e*(c + d*x))^(1/3)*(b*(c + d*x)^(2/3)*Cos[a + b*(c + d*x)^(2/3)] - Sin[a + b*(c + d*x)^(2/3)]))/(2*b^2*d*(c + d*x)^(1/3))","A",1
238,1,44,44,0.0698283,"\int \frac{\sin \left(a+b (c+d x)^{2/3}\right)}{\sqrt[3]{c e+d e x}} \, dx","Integrate[Sin[a + b*(c + d*x)^(2/3)]/(c*e + d*e*x)^(1/3),x]","-\frac{3 \sqrt[3]{c+d x} \cos \left(a+b (c+d x)^{2/3}\right)}{2 b d \sqrt[3]{e (c+d x)}}","-\frac{3 \sqrt[3]{c+d x} \cos \left(a+b (c+d x)^{2/3}\right)}{2 b d \sqrt[3]{e (c+d x)}}",1,"(-3*(c + d*x)^(1/3)*Cos[a + b*(c + d*x)^(2/3)])/(2*b*d*(e*(c + d*x))^(1/3))","A",1
239,1,96,133,0.1461254,"\int \frac{\sin \left(a+b (c+d x)^{2/3}\right)}{(c e+d e x)^{2/3}} \, dx","Integrate[Sin[a + b*(c + d*x)^(2/3)]/(c*e + d*e*x)^(2/3),x]","\frac{3 \sqrt{\frac{\pi }{2}} (c+d x)^{2/3} \left(\sin (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[3]{c+d x}\right)+\cos (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[3]{c+d x}\right)\right)}{\sqrt{b} d (e (c+d x))^{2/3}}","\frac{3 \sqrt{\frac{\pi }{2}} \sin (a) (c+d x)^{2/3} C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[3]{c+d x}\right)}{\sqrt{b} d (e (c+d x))^{2/3}}+\frac{3 \sqrt{\frac{\pi }{2}} \cos (a) (c+d x)^{2/3} S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[3]{c+d x}\right)}{\sqrt{b} d (e (c+d x))^{2/3}}",1,"(3*Sqrt[Pi/2]*(c + d*x)^(2/3)*(Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)^(1/3)] + FresnelC[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)^(1/3)]*Sin[a]))/(Sqrt[b]*d*(e*(c + d*x))^(2/3))","A",1
240,1,133,168,0.2434848,"\int \frac{\sin \left(a+b (c+d x)^{2/3}\right)}{(c e+d e x)^{4/3}} \, dx","Integrate[Sin[a + b*(c + d*x)^(2/3)]/(c*e + d*e*x)^(4/3),x]","-\frac{3 \left(\sqrt{2 \pi } \left(-\sqrt{b}\right) \cos (a) \sqrt[3]{c+d x} C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[3]{c+d x}\right)+\sqrt{2 \pi } \sqrt{b} \sin (a) \sqrt[3]{c+d x} S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[3]{c+d x}\right)+\sin \left(a+b (c+d x)^{2/3}\right)\right)}{d e \sqrt[3]{e (c+d x)}}","\frac{3 \sqrt{2 \pi } \sqrt{b} \cos (a) \sqrt[3]{c+d x} C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[3]{c+d x}\right)}{d e \sqrt[3]{e (c+d x)}}-\frac{3 \sqrt{2 \pi } \sqrt{b} \sin (a) \sqrt[3]{c+d x} S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} \sqrt[3]{c+d x}\right)}{d e \sqrt[3]{e (c+d x)}}-\frac{3 \sin \left(a+b (c+d x)^{2/3}\right)}{d e \sqrt[3]{e (c+d x)}}",1,"(-3*(-(Sqrt[b]*Sqrt[2*Pi]*(c + d*x)^(1/3)*Cos[a]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)^(1/3)]) + Sqrt[b]*Sqrt[2*Pi]*(c + d*x)^(1/3)*FresnelS[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)^(1/3)]*Sin[a] + Sin[a + b*(c + d*x)^(2/3)]))/(d*e*(e*(c + d*x))^(1/3))","A",1
241,1,87,126,0.1610206,"\int \frac{\sin \left(a+b (c+d x)^{2/3}\right)}{(c e+d e x)^{5/3}} \, dx","Integrate[Sin[a + b*(c + d*x)^(2/3)]/(c*e + d*e*x)^(5/3),x]","-\frac{3 \left(-b \cos (a) (c+d x)^{2/3} \text{Ci}\left(b (c+d x)^{2/3}\right)+b \sin (a) (c+d x)^{2/3} \text{Si}\left(b (c+d x)^{2/3}\right)+\sin \left(a+b (c+d x)^{2/3}\right)\right)}{2 d e (e (c+d x))^{2/3}}","\frac{3 b \cos (a) (c+d x)^{2/3} \text{Ci}\left(b (c+d x)^{2/3}\right)}{2 d e (e (c+d x))^{2/3}}-\frac{3 b \sin (a) (c+d x)^{2/3} \text{Si}\left(b (c+d x)^{2/3}\right)}{2 d e (e (c+d x))^{2/3}}-\frac{3 \sin \left(a+b (c+d x)^{2/3}\right)}{2 d e (e (c+d x))^{2/3}}",1,"(-3*(-(b*(c + d*x)^(2/3)*Cos[a]*CosIntegral[b*(c + d*x)^(2/3)]) + Sin[a + b*(c + d*x)^(2/3)] + b*(c + d*x)^(2/3)*Sin[a]*SinIntegral[b*(c + d*x)^(2/3)]))/(2*d*e*(e*(c + d*x))^(2/3))","A",1
242,1,208,247,0.3962136,"\int \sqrt[3]{c e+d e x} \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right) \, dx","Integrate[(c*e + d*e*x)^(1/3)*Sin[a + b/(c + d*x)^(1/3)],x]","-\frac{\sqrt[3]{e (c+d x)} \left(b^4 \sin (a) \text{Ci}\left(\frac{b}{\sqrt[3]{c+d x}}\right)+b^4 \cos (a) \text{Si}\left(\frac{b}{\sqrt[3]{c+d x}}\right)+b^3 \sqrt[3]{c+d x} \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)+b^2 (c+d x)^{2/3} \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)-6 c \sqrt[3]{c+d x} \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)-6 d x \sqrt[3]{c+d x} \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)-2 b c \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)-2 b d x \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)\right)}{8 d \sqrt[3]{c+d x}}","-\frac{b^4 \sin (a) \sqrt[3]{e (c+d x)} \text{Ci}\left(\frac{b}{\sqrt[3]{c+d x}}\right)}{8 d \sqrt[3]{c+d x}}-\frac{b^4 \cos (a) \sqrt[3]{e (c+d x)} \text{Si}\left(\frac{b}{\sqrt[3]{c+d x}}\right)}{8 d \sqrt[3]{c+d x}}-\frac{b^3 \sqrt[3]{e (c+d x)} \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{8 d}-\frac{b^2 \sqrt[3]{c+d x} \sqrt[3]{e (c+d x)} \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{8 d}+\frac{3 (c+d x) \sqrt[3]{e (c+d x)} \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{4 d}+\frac{b (c+d x)^{2/3} \sqrt[3]{e (c+d x)} \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{4 d}",1,"-1/8*((e*(c + d*x))^(1/3)*(-2*b*c*Cos[a + b/(c + d*x)^(1/3)] - 2*b*d*x*Cos[a + b/(c + d*x)^(1/3)] + b^3*(c + d*x)^(1/3)*Cos[a + b/(c + d*x)^(1/3)] + b^4*CosIntegral[b/(c + d*x)^(1/3)]*Sin[a] - 6*c*(c + d*x)^(1/3)*Sin[a + b/(c + d*x)^(1/3)] - 6*d*x*(c + d*x)^(1/3)*Sin[a + b/(c + d*x)^(1/3)] + b^2*(c + d*x)^(2/3)*Sin[a + b/(c + d*x)^(1/3)] + b^4*Cos[a]*SinIntegral[b/(c + d*x)^(1/3)]))/(d*(c + d*x)^(1/3))","A",1
243,1,131,168,0.184864,"\int \frac{\sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{\sqrt[3]{c e+d e x}} \, dx","Integrate[Sin[a + b/(c + d*x)^(1/3)]/(c*e + d*e*x)^(1/3),x]","\frac{3 \left(b^2 \sin (a) \sqrt[3]{c+d x} \text{Ci}\left(\frac{b}{\sqrt[3]{c+d x}}\right)+b^2 \cos (a) \sqrt[3]{c+d x} \text{Si}\left(\frac{b}{\sqrt[3]{c+d x}}\right)+c \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)+d x \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)+b (c+d x)^{2/3} \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)\right)}{2 d \sqrt[3]{e (c+d x)}}","\frac{3 b^2 \sin (a) \sqrt[3]{c+d x} \text{Ci}\left(\frac{b}{\sqrt[3]{c+d x}}\right)}{2 d \sqrt[3]{e (c+d x)}}+\frac{3 b^2 \cos (a) \sqrt[3]{c+d x} \text{Si}\left(\frac{b}{\sqrt[3]{c+d x}}\right)}{2 d \sqrt[3]{e (c+d x)}}+\frac{3 (c+d x) \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{2 d \sqrt[3]{e (c+d x)}}+\frac{3 b (c+d x)^{2/3} \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{2 d \sqrt[3]{e (c+d x)}}",1,"(3*(b*(c + d*x)^(2/3)*Cos[a + b/(c + d*x)^(1/3)] + b^2*(c + d*x)^(1/3)*CosIntegral[b/(c + d*x)^(1/3)]*Sin[a] + c*Sin[a + b/(c + d*x)^(1/3)] + d*x*Sin[a + b/(c + d*x)^(1/3)] + b^2*(c + d*x)^(1/3)*Cos[a]*SinIntegral[b/(c + d*x)^(1/3)]))/(2*d*(e*(c + d*x))^(1/3))","A",1
244,1,88,116,0.1853226,"\int \frac{\sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{(c e+d e x)^{2/3}} \, dx","Integrate[Sin[a + b/(c + d*x)^(1/3)]/(c*e + d*e*x)^(2/3),x]","\frac{3 \left(-b \cos (a) (c+d x)^{2/3} \text{Ci}\left(\frac{b}{\sqrt[3]{c+d x}}\right)+b \sin (a) (c+d x)^{2/3} \text{Si}\left(\frac{b}{\sqrt[3]{c+d x}}\right)+(c+d x) \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)\right)}{d (e (c+d x))^{2/3}}","-\frac{3 b \cos (a) (c+d x)^{2/3} \text{Ci}\left(\frac{b}{\sqrt[3]{c+d x}}\right)}{d (e (c+d x))^{2/3}}+\frac{3 b \sin (a) (c+d x)^{2/3} \text{Si}\left(\frac{b}{\sqrt[3]{c+d x}}\right)}{d (e (c+d x))^{2/3}}+\frac{3 (c+d x) \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{d (e (c+d x))^{2/3}}",1,"(3*(-(b*(c + d*x)^(2/3)*Cos[a]*CosIntegral[b/(c + d*x)^(1/3)]) + (c + d*x)*Sin[a + b/(c + d*x)^(1/3)] + b*(c + d*x)^(2/3)*Sin[a]*SinIntegral[b/(c + d*x)^(1/3)]))/(d*(e*(c + d*x))^(2/3))","A",1
245,1,42,45,0.064658,"\int \frac{\sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{(c e+d e x)^{4/3}} \, dx","Integrate[Sin[a + b/(c + d*x)^(1/3)]/(c*e + d*e*x)^(4/3),x]","\frac{3 (c+d x)^{4/3} \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{b d (e (c+d x))^{4/3}}","\frac{3 \sqrt[3]{c+d x} \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{b d e \sqrt[3]{e (c+d x)}}",1,"(3*(c + d*x)^(4/3)*Cos[a + b/(c + d*x)^(1/3)])/(b*d*(e*(c + d*x))^(4/3))","A",1
246,1,72,91,0.0892156,"\int \frac{\sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{(c e+d e x)^{5/3}} \, dx","Integrate[Sin[a + b/(c + d*x)^(1/3)]/(c*e + d*e*x)^(5/3),x]","\frac{3 (c+d x)^{5/3} \left(\frac{\cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{b \sqrt[3]{c+d x}}-\frac{\sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{b^2}\right)}{d (e (c+d x))^{5/3}}","\frac{3 \sqrt[3]{c+d x} \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{b d e (e (c+d x))^{2/3}}-\frac{3 (c+d x)^{2/3} \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{b^2 d e (e (c+d x))^{2/3}}",1,"(3*(c + d*x)^(5/3)*(Cos[a + b/(c + d*x)^(1/3)]/(b*(c + d*x)^(1/3)) - Sin[a + b/(c + d*x)^(1/3)]/b^2))/(d*(e*(c + d*x))^(5/3))","A",1
247,1,107,172,0.1682105,"\int \frac{\sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{(c e+d e x)^{7/3}} \, dx","Integrate[Sin[a + b/(c + d*x)^(1/3)]/(c*e + d*e*x)^(7/3),x]","-\frac{3 \left(\left(6 b (c+d x)-b^3 \sqrt[3]{c+d x}\right) \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)+3 \sqrt[3]{c+d x} \left(b^2 \sqrt[3]{c+d x}-2 c-2 d x\right) \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)\right)}{b^4 d e (e (c+d x))^{4/3}}","\frac{18 \sqrt[3]{c+d x} \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{b^4 d e^2 \sqrt[3]{e (c+d x)}}-\frac{18 \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{b^3 d e^2 \sqrt[3]{e (c+d x)}}-\frac{9 \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{b^2 d e^2 \sqrt[3]{c+d x} \sqrt[3]{e (c+d x)}}+\frac{3 \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{b d e^2 (c+d x)^{2/3} \sqrt[3]{e (c+d x)}}",1,"(-3*((-(b^3*(c + d*x)^(1/3)) + 6*b*(c + d*x))*Cos[a + b/(c + d*x)^(1/3)] + 3*(c + d*x)^(1/3)*(-2*c - 2*d*x + b^2*(c + d*x)^(1/3))*Sin[a + b/(c + d*x)^(1/3)]))/(b^4*d*e*(e*(c + d*x))^(4/3))","A",1
248,1,112,217,0.2953465,"\int \frac{\sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{(c e+d e x)^{8/3}} \, dx","Integrate[Sin[a + b/(c + d*x)^(1/3)]/(c*e + d*e*x)^(8/3),x]","\frac{(c+d x)^{4/3} \left(12 b \left(b^2 \left(-\sqrt[3]{c+d x}\right)+6 c+6 d x\right) \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)+3 \left(b^4-12 b^2 (c+d x)^{2/3}+24 (c+d x)^{4/3}\right) \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)\right)}{b^5 d (e (c+d x))^{8/3}}","\frac{72 (c+d x)^{2/3} \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{b^5 d e^2 (e (c+d x))^{2/3}}+\frac{72 \sqrt[3]{c+d x} \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{b^4 d e^2 (e (c+d x))^{2/3}}-\frac{36 \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{b^3 d e^2 (e (c+d x))^{2/3}}-\frac{12 \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{b^2 d e^2 \sqrt[3]{c+d x} (e (c+d x))^{2/3}}+\frac{3 \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{b d e^2 (c+d x)^{2/3} (e (c+d x))^{2/3}}",1,"((c + d*x)^(4/3)*(3*(b^4 - 12*b^2*(c + d*x)^(2/3) + 24*(c + d*x)^(4/3))*Cos[a + b/(c + d*x)^(1/3)] + 12*b*(6*c + 6*d*x - b^2*(c + d*x)^(1/3))*Sin[a + b/(c + d*x)^(1/3)]))/(b^5*d*(e*(c + d*x))^(8/3))","A",1
249,1,237,299,0.9034222,"\int (c e+d e x)^{4/3} \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right) \, dx","Integrate[(c*e + d*e*x)^(4/3)*Sin[a + b/(c + d*x)^(2/3)],x]","\frac{(e (c+d x))^{4/3} \left(-\frac{8 \sqrt{2 \pi } b^{7/2} \left(\sin (a) C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)+\cos (a) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)\right)}{(c+d x)^{4/3}}+\frac{\cos \left(\frac{b}{(c+d x)^{2/3}}\right) \left(-8 b^3 \cos (a)-4 b^2 \sin (a) (c+d x)^{2/3}+6 b \cos (a) (c+d x)^{4/3}+15 \sin (a) (c+d x)^2\right)}{c+d x}+\frac{\sin \left(\frac{b}{(c+d x)^{2/3}}\right) \left(8 b^3 \sin (a)-4 b^2 \cos (a) (c+d x)^{2/3}-6 b \sin (a) (c+d x)^{4/3}+15 \cos (a) (c+d x)^2\right)}{c+d x}\right)}{35 d}","-\frac{8 \sqrt{2 \pi } b^{7/2} e \sin (a) \sqrt[3]{e (c+d x)} C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)}{35 d \sqrt[3]{c+d x}}-\frac{8 \sqrt{2 \pi } b^{7/2} e \cos (a) \sqrt[3]{e (c+d x)} S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)}{35 d \sqrt[3]{c+d x}}-\frac{8 b^3 e \sqrt[3]{e (c+d x)} \cos \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{35 d}-\frac{4 b^2 e (c+d x)^{2/3} \sqrt[3]{e (c+d x)} \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{35 d}+\frac{3 e (c+d x)^2 \sqrt[3]{e (c+d x)} \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{7 d}+\frac{6 b e (c+d x)^{4/3} \sqrt[3]{e (c+d x)} \cos \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{35 d}",1,"((e*(c + d*x))^(4/3)*((Cos[b/(c + d*x)^(2/3)]*(-8*b^3*Cos[a] + 6*b*(c + d*x)^(4/3)*Cos[a] - 4*b^2*(c + d*x)^(2/3)*Sin[a] + 15*(c + d*x)^2*Sin[a]))/(c + d*x) - (8*b^(7/2)*Sqrt[2*Pi]*(Cos[a]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)^(1/3)] + FresnelC[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)^(1/3)]*Sin[a]))/(c + d*x)^(4/3) + ((-4*b^2*(c + d*x)^(2/3)*Cos[a] + 15*(c + d*x)^2*Cos[a] + 8*b^3*Sin[a] - 6*b*(c + d*x)^(4/3)*Sin[a])*Sin[b/(c + d*x)^(2/3)])/(c + d*x)))/(35*d)","A",1
250,1,228,262,0.3532565,"\int (c e+d e x)^{2/3} \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right) \, dx","Integrate[(c*e + d*e*x)^(2/3)*Sin[a + b/(c + d*x)^(2/3)],x]","\frac{(e (c+d x))^{2/3} \left(4 \sqrt{2 \pi } b^{5/2} \cos (a) C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)-4 \sqrt{2 \pi } b^{5/2} \sin (a) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)-4 b^2 \sqrt[3]{c+d x} \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)+3 c (c+d x)^{2/3} \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)+3 d x (c+d x)^{2/3} \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)+2 b c \cos \left(a+\frac{b}{(c+d x)^{2/3}}\right)+2 b d x \cos \left(a+\frac{b}{(c+d x)^{2/3}}\right)\right)}{5 d (c+d x)^{2/3}}","\frac{4 \sqrt{2} \sqrt{\pi } b^{5/2} \cos (a) (e (c+d x))^{2/3} C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)}{5 d (c+d x)^{2/3}}-\frac{4 \sqrt{2} \sqrt{\pi } b^{5/2} \sin (a) (e (c+d x))^{2/3} S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)}{5 d (c+d x)^{2/3}}-\frac{4 b^2 (e (c+d x))^{2/3} \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{5 d \sqrt[3]{c+d x}}+\frac{3 (c+d x) (e (c+d x))^{2/3} \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{5 d}+\frac{2 b \sqrt[3]{c+d x} (e (c+d x))^{2/3} \cos \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{5 d}",1,"((e*(c + d*x))^(2/3)*(2*b*c*Cos[a + b/(c + d*x)^(2/3)] + 2*b*d*x*Cos[a + b/(c + d*x)^(2/3)] + 4*b^(5/2)*Sqrt[2*Pi]*Cos[a]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)^(1/3)] - 4*b^(5/2)*Sqrt[2*Pi]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)^(1/3)]*Sin[a] - 4*b^2*(c + d*x)^(1/3)*Sin[a + b/(c + d*x)^(2/3)] + 3*c*(c + d*x)^(2/3)*Sin[a + b/(c + d*x)^(2/3)] + 3*d*x*(c + d*x)^(2/3)*Sin[a + b/(c + d*x)^(2/3)]))/(5*d*(c + d*x)^(2/3))","A",1
251,1,113,168,0.3068949,"\int \sqrt[3]{c e+d e x} \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right) \, dx","Integrate[(c*e + d*e*x)^(1/3)*Sin[a + b/(c + d*x)^(2/3)],x]","\frac{3 \sqrt[3]{e (c+d x)} \left(b^2 \sin (a) \text{Ci}\left(\frac{b}{(c+d x)^{2/3}}\right)+b^2 \cos (a) \text{Si}\left(\frac{b}{(c+d x)^{2/3}}\right)+(c+d x)^{4/3} \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)+b (c+d x)^{2/3} \cos \left(a+\frac{b}{(c+d x)^{2/3}}\right)\right)}{4 d \sqrt[3]{c+d x}}","\frac{3 b^2 \sin (a) \sqrt[3]{e (c+d x)} \text{Ci}\left(\frac{b}{(c+d x)^{2/3}}\right)}{4 d \sqrt[3]{c+d x}}+\frac{3 b^2 \cos (a) \sqrt[3]{e (c+d x)} \text{Si}\left(\frac{b}{(c+d x)^{2/3}}\right)}{4 d \sqrt[3]{c+d x}}+\frac{3 (c+d x) \sqrt[3]{e (c+d x)} \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{4 d}+\frac{3 b \sqrt[3]{c+d x} \sqrt[3]{e (c+d x)} \cos \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{4 d}",1,"(3*(e*(c + d*x))^(1/3)*(b*(c + d*x)^(2/3)*Cos[a + b/(c + d*x)^(2/3)] + b^2*CosIntegral[b/(c + d*x)^(2/3)]*Sin[a] + (c + d*x)^(4/3)*Sin[a + b/(c + d*x)^(2/3)] + b^2*Cos[a]*SinIntegral[b/(c + d*x)^(2/3)]))/(4*d*(c + d*x)^(1/3))","A",1
252,1,90,122,0.2280516,"\int \frac{\sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{\sqrt[3]{c e+d e x}} \, dx","Integrate[Sin[a + b/(c + d*x)^(2/3)]/(c*e + d*e*x)^(1/3),x]","\frac{3 \left(-b \cos (a) \sqrt[3]{c+d x} \text{Ci}\left(\frac{b}{(c+d x)^{2/3}}\right)+b \sin (a) \sqrt[3]{c+d x} \text{Si}\left(\frac{b}{(c+d x)^{2/3}}\right)+(c+d x) \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)\right)}{2 d \sqrt[3]{e (c+d x)}}","-\frac{3 b \cos (a) \sqrt[3]{c+d x} \text{Ci}\left(\frac{b}{(c+d x)^{2/3}}\right)}{2 d \sqrt[3]{e (c+d x)}}+\frac{3 b \sin (a) \sqrt[3]{c+d x} \text{Si}\left(\frac{b}{(c+d x)^{2/3}}\right)}{2 d \sqrt[3]{e (c+d x)}}+\frac{3 (c+d x) \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{2 d \sqrt[3]{e (c+d x)}}",1,"(3*(-(b*(c + d*x)^(1/3)*Cos[a]*CosIntegral[b/(c + d*x)^(2/3)]) + (c + d*x)*Sin[a + b/(c + d*x)^(2/3)] + b*(c + d*x)^(1/3)*Sin[a]*SinIntegral[b/(c + d*x)^(2/3)]))/(2*d*(e*(c + d*x))^(1/3))","A",1
253,1,136,164,0.3174424,"\int \frac{\sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{(c e+d e x)^{2/3}} \, dx","Integrate[Sin[a + b/(c + d*x)^(2/3)]/(c*e + d*e*x)^(2/3),x]","\frac{3 \left(\sqrt{2 \pi } \left(-\sqrt{b}\right) \cos (a) (c+d x)^{2/3} C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)+\sqrt{2 \pi } \sqrt{b} \sin (a) (c+d x)^{2/3} S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)+(c+d x) \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)\right)}{d (e (c+d x))^{2/3}}","-\frac{3 \sqrt{2 \pi } \sqrt{b} \cos (a) (c+d x)^{2/3} C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)}{d (e (c+d x))^{2/3}}+\frac{3 \sqrt{2 \pi } \sqrt{b} \sin (a) (c+d x)^{2/3} S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)}{d (e (c+d x))^{2/3}}+\frac{3 (c+d x) \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{d (e (c+d x))^{2/3}}",1,"(3*(-(Sqrt[b]*Sqrt[2*Pi]*(c + d*x)^(2/3)*Cos[a]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)^(1/3)]) + Sqrt[b]*Sqrt[2*Pi]*(c + d*x)^(2/3)*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)^(1/3)]*Sin[a] + (c + d*x)*Sin[a + b/(c + d*x)^(2/3)]))/(d*(e*(c + d*x))^(2/3))","A",1
254,1,96,141,0.1599929,"\int \frac{\sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{(c e+d e x)^{4/3}} \, dx","Integrate[Sin[a + b/(c + d*x)^(2/3)]/(c*e + d*e*x)^(4/3),x]","-\frac{3 \sqrt{\frac{\pi }{2}} (c+d x)^{4/3} \left(\sin (a) C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)+\cos (a) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)\right)}{\sqrt{b} d (e (c+d x))^{4/3}}","-\frac{3 \sqrt{\pi } \sin (a) \sqrt[3]{c+d x} C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)}{\sqrt{2} \sqrt{b} d e \sqrt[3]{e (c+d x)}}-\frac{3 \sqrt{\pi } \cos (a) \sqrt[3]{c+d x} S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)}{\sqrt{2} \sqrt{b} d e \sqrt[3]{e (c+d x)}}",1,"(-3*Sqrt[Pi/2]*(c + d*x)^(4/3)*(Cos[a]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)^(1/3)] + FresnelC[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)^(1/3)]*Sin[a]))/(Sqrt[b]*d*(e*(c + d*x))^(4/3))","A",1
255,1,44,47,0.0713861,"\int \frac{\sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{(c e+d e x)^{5/3}} \, dx","Integrate[Sin[a + b/(c + d*x)^(2/3)]/(c*e + d*e*x)^(5/3),x]","\frac{3 (c+d x)^{5/3} \cos \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{2 b d (e (c+d x))^{5/3}}","\frac{3 (c+d x)^{2/3} \cos \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{2 b d e (e (c+d x))^{2/3}}",1,"(3*(c + d*x)^(5/3)*Cos[a + b/(c + d*x)^(2/3)])/(2*b*d*(e*(c + d*x))^(5/3))","A",1
256,1,72,95,0.1062422,"\int \frac{\sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{(c e+d e x)^{7/3}} \, dx","Integrate[Sin[a + b/(c + d*x)^(2/3)]/(c*e + d*e*x)^(7/3),x]","-\frac{3 (c+d x)^{5/3} \left((c+d x)^{2/3} \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)-b \cos \left(a+\frac{b}{(c+d x)^{2/3}}\right)\right)}{2 b^2 d (e (c+d x))^{7/3}}","\frac{3 \cos \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{2 b d e^2 \sqrt[3]{c+d x} \sqrt[3]{e (c+d x)}}-\frac{3 \sqrt[3]{c+d x} \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{2 b^2 d e^2 \sqrt[3]{e (c+d x)}}",1,"(-3*(c + d*x)^(5/3)*(-(b*Cos[a + b/(c + d*x)^(2/3)]) + (c + d*x)^(2/3)*Sin[a + b/(c + d*x)^(2/3)]))/(2*b^2*d*(e*(c + d*x))^(7/3))","A",1
257,1,165,237,0.9127421,"\int \frac{\sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{(c e+d e x)^{8/3}} \, dx","Integrate[Sin[a + b/(c + d*x)^(2/3)]/(c*e + d*e*x)^(8/3),x]","\frac{(c+d x)^{5/3} \left(9 \sqrt{2 \pi } \sin (a) (c+d x) C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)+9 \sqrt{2 \pi } \cos (a) (c+d x) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)+6 \sqrt{b} \left(2 b \cos \left(a+\frac{b}{(c+d x)^{2/3}}\right)-3 (c+d x)^{2/3} \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)\right)\right)}{8 b^{5/2} d (e (c+d x))^{8/3}}","\frac{9 \sqrt{\frac{\pi }{2}} \sin (a) (c+d x)^{2/3} C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)}{4 b^{5/2} d e^2 (e (c+d x))^{2/3}}+\frac{9 \sqrt{\frac{\pi }{2}} \cos (a) (c+d x)^{2/3} S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)}{4 b^{5/2} d e^2 (e (c+d x))^{2/3}}-\frac{9 \sqrt[3]{c+d x} \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{4 b^2 d e^2 (e (c+d x))^{2/3}}+\frac{3 \cos \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{2 b d e^2 \sqrt[3]{c+d x} (e (c+d x))^{2/3}}",1,"((c + d*x)^(5/3)*(9*Sqrt[2*Pi]*(c + d*x)*Cos[a]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)^(1/3)] + 9*Sqrt[2*Pi]*(c + d*x)*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)^(1/3)]*Sin[a] + 6*Sqrt[b]*(2*b*Cos[a + b/(c + d*x)^(2/3)] - 3*(c + d*x)^(2/3)*Sin[a + b/(c + d*x)^(2/3)])))/(8*b^(5/2)*d*(e*(c + d*x))^(8/3))","A",1
258,1,192,277,1.2747346,"\int \frac{\sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{(c e+d e x)^{10/3}} \, dx","Integrate[Sin[a + b/(c + d*x)^(2/3)]/(c*e + d*e*x)^(10/3),x]","\frac{(e (c+d x))^{2/3} \left(-6 \sqrt{b} \left(\left(15 (c+d x)^{4/3}-4 b^2\right) \cos \left(a+\frac{b}{(c+d x)^{2/3}}\right)+10 b (c+d x)^{2/3} \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)\right)+45 \sqrt{2 \pi } \cos (a) (c+d x)^{5/3} C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)-45 \sqrt{2 \pi } \sin (a) (c+d x)^{5/3} S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)\right)}{16 b^{7/2} d e^4 (c+d x)^{7/3}}","\frac{45 \sqrt{\pi } \cos (a) \sqrt[3]{c+d x} C\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)}{8 \sqrt{2} b^{7/2} d e^3 \sqrt[3]{e (c+d x)}}-\frac{45 \sqrt{\pi } \sin (a) \sqrt[3]{c+d x} S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{\sqrt[3]{c+d x}}\right)}{8 \sqrt{2} b^{7/2} d e^3 \sqrt[3]{e (c+d x)}}-\frac{45 \cos \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{8 b^3 d e^3 \sqrt[3]{e (c+d x)}}-\frac{15 \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{4 b^2 d e^3 (c+d x)^{2/3} \sqrt[3]{e (c+d x)}}+\frac{3 \cos \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{2 b d e^3 (c+d x)^{4/3} \sqrt[3]{e (c+d x)}}",1,"((e*(c + d*x))^(2/3)*(45*Sqrt[2*Pi]*(c + d*x)^(5/3)*Cos[a]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)^(1/3)] - 45*Sqrt[2*Pi]*(c + d*x)^(5/3)*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)^(1/3)]*Sin[a] - 6*Sqrt[b]*((-4*b^2 + 15*(c + d*x)^(4/3))*Cos[a + b/(c + d*x)^(2/3)] + 10*b*(c + d*x)^(2/3)*Sin[a + b/(c + d*x)^(2/3)])))/(16*b^(7/2)*d*e^4*(c + d*x)^(7/3))","A",1
259,0,0,21,6.1800719,"\int (e x)^m \sin \left(a+b (c+d x)^n\right) \, dx","Integrate[(e*x)^m*Sin[a + b*(c + d*x)^n],x]","\int (e x)^m \sin \left(a+b (c+d x)^n\right) \, dx","\text{Int}\left((e x)^m \sin \left(a+b (c+d x)^n\right),x\right)",0,"Integrate[(e*x)^m*Sin[a + b*(c + d*x)^n], x]","A",-1
260,0,0,503,12.2202774,"\int x^3 \sin \left(a+b (c+d x)^n\right) \, dx","Integrate[x^3*Sin[a + b*(c + d*x)^n],x]","\int x^3 \sin \left(a+b (c+d x)^n\right) \, dx","-\frac{i e^{i a} c^3 (c+d x) \left(-i b (c+d x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-i b (c+d x)^n\right)}{2 d^4 n}+\frac{i e^{-i a} c^3 (c+d x) \left(i b (c+d x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},i b (c+d x)^n\right)}{2 d^4 n}+\frac{3 i e^{i a} c^2 (c+d x)^2 \left(-i b (c+d x)^n\right)^{-2/n} \Gamma \left(\frac{2}{n},-i b (c+d x)^n\right)}{2 d^4 n}-\frac{3 i e^{-i a} c^2 (c+d x)^2 \left(i b (c+d x)^n\right)^{-2/n} \Gamma \left(\frac{2}{n},i b (c+d x)^n\right)}{2 d^4 n}+\frac{i e^{i a} (c+d x)^4 \left(-i b (c+d x)^n\right)^{-4/n} \Gamma \left(\frac{4}{n},-i b (c+d x)^n\right)}{2 d^4 n}-\frac{3 i e^{i a} c (c+d x)^3 \left(-i b (c+d x)^n\right)^{-3/n} \Gamma \left(\frac{3}{n},-i b (c+d x)^n\right)}{2 d^4 n}+\frac{3 i e^{-i a} c (c+d x)^3 \left(i b (c+d x)^n\right)^{-3/n} \Gamma \left(\frac{3}{n},i b (c+d x)^n\right)}{2 d^4 n}-\frac{i e^{-i a} (c+d x)^4 \left(i b (c+d x)^n\right)^{-4/n} \Gamma \left(\frac{4}{n},i b (c+d x)^n\right)}{2 d^4 n}",1,"Integrate[x^3*Sin[a + b*(c + d*x)^n], x]","F",-1
261,0,0,369,8.7740805,"\int x^2 \sin \left(a+b (c+d x)^n\right) \, dx","Integrate[x^2*Sin[a + b*(c + d*x)^n],x]","\int x^2 \sin \left(a+b (c+d x)^n\right) \, dx","\frac{i e^{i a} c^2 (c+d x) \left(-i b (c+d x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-i b (c+d x)^n\right)}{2 d^3 n}-\frac{i e^{-i a} c^2 (c+d x) \left(i b (c+d x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},i b (c+d x)^n\right)}{2 d^3 n}+\frac{i e^{i a} (c+d x)^3 \left(-i b (c+d x)^n\right)^{-3/n} \Gamma \left(\frac{3}{n},-i b (c+d x)^n\right)}{2 d^3 n}-\frac{i e^{i a} c (c+d x)^2 \left(-i b (c+d x)^n\right)^{-2/n} \Gamma \left(\frac{2}{n},-i b (c+d x)^n\right)}{d^3 n}+\frac{i e^{-i a} c (c+d x)^2 \left(i b (c+d x)^n\right)^{-2/n} \Gamma \left(\frac{2}{n},i b (c+d x)^n\right)}{d^3 n}-\frac{i e^{-i a} (c+d x)^3 \left(i b (c+d x)^n\right)^{-3/n} \Gamma \left(\frac{3}{n},i b (c+d x)^n\right)}{2 d^3 n}",1,"Integrate[x^2*Sin[a + b*(c + d*x)^n], x]","F",-1
262,1,192,243,0.8605276,"\int x \sin \left(a+b (c+d x)^n\right) \, dx","Integrate[x*Sin[a + b*(c + d*x)^n],x]","\frac{(c+d x) \left((\sin (a)-i \cos (a)) \left(-i b (c+d x)^n\right)^{-2/n} \left(c \left(-i b (c+d x)^n\right)^{\frac{1}{n}} \Gamma \left(\frac{1}{n},-i b (c+d x)^n\right)-(c+d x) \Gamma \left(\frac{2}{n},-i b (c+d x)^n\right)\right)+(\sin (a)+i \cos (a)) \left(i b (c+d x)^n\right)^{-2/n} \left(c \left(i b (c+d x)^n\right)^{\frac{1}{n}} \Gamma \left(\frac{1}{n},i b (c+d x)^n\right)-(c+d x) \Gamma \left(\frac{2}{n},i b (c+d x)^n\right)\right)\right)}{2 d^2 n}","\frac{i e^{i a} (c+d x)^2 \left(-i b (c+d x)^n\right)^{-2/n} \Gamma \left(\frac{2}{n},-i b (c+d x)^n\right)}{2 d^2 n}-\frac{i e^{i a} c (c+d x) \left(-i b (c+d x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-i b (c+d x)^n\right)}{2 d^2 n}+\frac{i e^{-i a} c (c+d x) \left(i b (c+d x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},i b (c+d x)^n\right)}{2 d^2 n}-\frac{i e^{-i a} (c+d x)^2 \left(i b (c+d x)^n\right)^{-2/n} \Gamma \left(\frac{2}{n},i b (c+d x)^n\right)}{2 d^2 n}",1,"((c + d*x)*(((c*((-I)*b*(c + d*x)^n)^n^(-1)*Gamma[n^(-1), (-I)*b*(c + d*x)^n] - (c + d*x)*Gamma[2/n, (-I)*b*(c + d*x)^n])*((-I)*Cos[a] + Sin[a]))/((-I)*b*(c + d*x)^n)^(2/n) + ((c*(I*b*(c + d*x)^n)^n^(-1)*Gamma[n^(-1), I*b*(c + d*x)^n] - (c + d*x)*Gamma[2/n, I*b*(c + d*x)^n])*(I*Cos[a] + Sin[a]))/(I*b*(c + d*x)^n)^(2/n)))/(2*d^2*n)","A",1
263,1,121,117,0.042021,"\int \sin \left(a+b (c+d x)^n\right) \, dx","Integrate[Sin[a + b*(c + d*x)^n],x]","\frac{i (\cos (a)+i \sin (a)) (c+d x) \left(-i b (c+d x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-i b (c+d x)^n\right)}{2 d n}-\frac{i (\cos (a)-i \sin (a)) (c+d x) \left(i b (c+d x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},i b (c+d x)^n\right)}{2 d n}","\frac{i e^{i a} (c+d x) \left(-i b (c+d x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-i b (c+d x)^n\right)}{2 d n}-\frac{i e^{-i a} (c+d x) \left(i b (c+d x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},i b (c+d x)^n\right)}{2 d n}",1,"((-1/2*I)*(c + d*x)*Gamma[n^(-1), I*b*(c + d*x)^n]*(Cos[a] - I*Sin[a]))/(d*n*(I*b*(c + d*x)^n)^n^(-1)) + ((I/2)*(c + d*x)*Gamma[n^(-1), (-I)*b*(c + d*x)^n]*(Cos[a] + I*Sin[a]))/(d*n*((-I)*b*(c + d*x)^n)^n^(-1))","A",1
264,0,0,19,1.9232576,"\int \frac{\sin \left(a+b (c+d x)^n\right)}{x} \, dx","Integrate[Sin[a + b*(c + d*x)^n]/x,x]","\int \frac{\sin \left(a+b (c+d x)^n\right)}{x} \, dx","\text{Int}\left(\frac{\sin \left(a+b (c+d x)^n\right)}{x},x\right)",0,"Integrate[Sin[a + b*(c + d*x)^n]/x, x]","A",-1
265,0,0,19,1.8015497,"\int \frac{\sin \left(a+b (c+d x)^n\right)}{x^2} \, dx","Integrate[Sin[a + b*(c + d*x)^n]/x^2,x]","\int \frac{\sin \left(a+b (c+d x)^n\right)}{x^2} \, dx","\text{Int}\left(\frac{\sin \left(a+b (c+d x)^n\right)}{x^2},x\right)",0,"Integrate[Sin[a + b*(c + d*x)^n]/x^2, x]","A",-1
266,1,539,519,15.1458791,"\int x^3 \left(a+b \sin \left(c+d (f+g x)^n\right)\right) \, dx","Integrate[x^3*(a + b*Sin[c + d*(f + g*x)^n]),x]","\frac{1}{4} \left(a x^4-\frac{2 i b (\cos (c)-i \sin (c)) (f+g x) \left(d^2 (f+g x)^{2 n}\right)^{-4/n} \left(f^3 (\cos (c)+i \sin (c))^2 \left(i d (f+g x)^n\right)^{4/n} \left(-i d (f+g x)^n\right)^{3/n} \Gamma \left(\frac{1}{n},-i d (f+g x)^n\right)-(f+g x) \left(3 f^2 (\cos (c)+i \sin (c))^2 \left(i d (f+g x)^n\right)^{4/n} \left(-i d (f+g x)^n\right)^{2/n} \Gamma \left(\frac{2}{n},-i d (f+g x)^n\right)-(f+g x) \left(3 f (\cos (c)+i \sin (c))^2 \left(i d (f+g x)^n\right)^{4/n} \left(-i d (f+g x)^n\right)^{\frac{1}{n}} \Gamma \left(\frac{3}{n},-i d (f+g x)^n\right)-(f+g x) \left((\cos (c)+i \sin (c))^2 \left(i d (f+g x)^n\right)^{4/n} \Gamma \left(\frac{4}{n},-i d (f+g x)^n\right)-\left(-i d (f+g x)^n\right)^{4/n} \Gamma \left(\frac{4}{n},i d (f+g x)^n\right)\right)-3 f \left(i d (f+g x)^n\right)^{\frac{1}{n}} \left(-i d (f+g x)^n\right)^{4/n} \Gamma \left(\frac{3}{n},i d (f+g x)^n\right)\right)-3 f^2 \left(i d (f+g x)^n\right)^{2/n} \left(-i d (f+g x)^n\right)^{4/n} \Gamma \left(\frac{2}{n},i d (f+g x)^n\right)\right)-f^3 \left(i d (f+g x)^n\right)^{3/n} \left(-i d (f+g x)^n\right)^{4/n} \Gamma \left(\frac{1}{n},i d (f+g x)^n\right)\right)}{g^4 n}\right)","\frac{a x^4}{4}-\frac{i b e^{i c} f^3 (f+g x) \left(-i d (f+g x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-i d (f+g x)^n\right)}{2 g^4 n}+\frac{i b e^{-i c} f^3 (f+g x) \left(i d (f+g x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},i d (f+g x)^n\right)}{2 g^4 n}+\frac{3 i b e^{i c} f^2 (f+g x)^2 \left(-i d (f+g x)^n\right)^{-2/n} \Gamma \left(\frac{2}{n},-i d (f+g x)^n\right)}{2 g^4 n}-\frac{3 i b e^{-i c} f^2 (f+g x)^2 \left(i d (f+g x)^n\right)^{-2/n} \Gamma \left(\frac{2}{n},i d (f+g x)^n\right)}{2 g^4 n}+\frac{i b e^{i c} (f+g x)^4 \left(-i d (f+g x)^n\right)^{-4/n} \Gamma \left(\frac{4}{n},-i d (f+g x)^n\right)}{2 g^4 n}-\frac{3 i b e^{i c} f (f+g x)^3 \left(-i d (f+g x)^n\right)^{-3/n} \Gamma \left(\frac{3}{n},-i d (f+g x)^n\right)}{2 g^4 n}+\frac{3 i b e^{-i c} f (f+g x)^3 \left(i d (f+g x)^n\right)^{-3/n} \Gamma \left(\frac{3}{n},i d (f+g x)^n\right)}{2 g^4 n}-\frac{i b e^{-i c} (f+g x)^4 \left(i d (f+g x)^n\right)^{-4/n} \Gamma \left(\frac{4}{n},i d (f+g x)^n\right)}{2 g^4 n}",1,"(a*x^4 - ((2*I)*b*(f + g*x)*(-(f^3*((-I)*d*(f + g*x)^n)^(4/n)*(I*d*(f + g*x)^n)^(3/n)*Gamma[n^(-1), I*d*(f + g*x)^n]) - (f + g*x)*(-3*f^2*((-I)*d*(f + g*x)^n)^(4/n)*(I*d*(f + g*x)^n)^(2/n)*Gamma[2/n, I*d*(f + g*x)^n] - (f + g*x)*(-3*f*((-I)*d*(f + g*x)^n)^(4/n)*(I*d*(f + g*x)^n)^n^(-1)*Gamma[3/n, I*d*(f + g*x)^n] - (f + g*x)*(-(((-I)*d*(f + g*x)^n)^(4/n)*Gamma[4/n, I*d*(f + g*x)^n]) + (I*d*(f + g*x)^n)^(4/n)*Gamma[4/n, (-I)*d*(f + g*x)^n]*(Cos[c] + I*Sin[c])^2) + 3*f*((-I)*d*(f + g*x)^n)^n^(-1)*(I*d*(f + g*x)^n)^(4/n)*Gamma[3/n, (-I)*d*(f + g*x)^n]*(Cos[c] + I*Sin[c])^2) + 3*f^2*((-I)*d*(f + g*x)^n)^(2/n)*(I*d*(f + g*x)^n)^(4/n)*Gamma[2/n, (-I)*d*(f + g*x)^n]*(Cos[c] + I*Sin[c])^2) + f^3*((-I)*d*(f + g*x)^n)^(3/n)*(I*d*(f + g*x)^n)^(4/n)*Gamma[n^(-1), (-I)*d*(f + g*x)^n]*(Cos[c] + I*Sin[c])^2)*(Cos[c] - I*Sin[c]))/(g^4*n*(d^2*(f + g*x)^(2*n))^(4/n)))/4","A",1
267,1,403,383,10.2332055,"\int x^2 \left(a+b \sin \left(c+d (f+g x)^n\right)\right) \, dx","Integrate[x^2*(a + b*Sin[c + d*(f + g*x)^n]),x]","\frac{a x^3}{3}+\frac{i b (\cos (c)-i \sin (c)) (f+g x) \left(d^2 (f+g x)^{2 n}\right)^{-3/n} \left(f^2 (\cos (c)+i \sin (c))^2 \left(i d (f+g x)^n\right)^{3/n} \left(-i d (f+g x)^n\right)^{2/n} \Gamma \left(\frac{1}{n},-i d (f+g x)^n\right)-(f+g x) \left(2 f (\cos (c)+i \sin (c))^2 \left(i d (f+g x)^n\right)^{3/n} \left(-i d (f+g x)^n\right)^{\frac{1}{n}} \Gamma \left(\frac{2}{n},-i d (f+g x)^n\right)-(f+g x) \left((\cos (c)+i \sin (c))^2 \left(i d (f+g x)^n\right)^{3/n} \Gamma \left(\frac{3}{n},-i d (f+g x)^n\right)-\left(-i d (f+g x)^n\right)^{3/n} \Gamma \left(\frac{3}{n},i d (f+g x)^n\right)\right)-2 f \left(i d (f+g x)^n\right)^{\frac{1}{n}} \left(-i d (f+g x)^n\right)^{3/n} \Gamma \left(\frac{2}{n},i d (f+g x)^n\right)\right)-f^2 \left(i d (f+g x)^n\right)^{2/n} \left(-i d (f+g x)^n\right)^{3/n} \Gamma \left(\frac{1}{n},i d (f+g x)^n\right)\right)}{2 g^3 n}","\frac{a x^3}{3}+\frac{i b e^{i c} f^2 (f+g x) \left(-i d (f+g x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-i d (f+g x)^n\right)}{2 g^3 n}-\frac{i b e^{-i c} f^2 (f+g x) \left(i d (f+g x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},i d (f+g x)^n\right)}{2 g^3 n}+\frac{i b e^{i c} (f+g x)^3 \left(-i d (f+g x)^n\right)^{-3/n} \Gamma \left(\frac{3}{n},-i d (f+g x)^n\right)}{2 g^3 n}-\frac{i b e^{i c} f (f+g x)^2 \left(-i d (f+g x)^n\right)^{-2/n} \Gamma \left(\frac{2}{n},-i d (f+g x)^n\right)}{g^3 n}+\frac{i b e^{-i c} f (f+g x)^2 \left(i d (f+g x)^n\right)^{-2/n} \Gamma \left(\frac{2}{n},i d (f+g x)^n\right)}{g^3 n}-\frac{i b e^{-i c} (f+g x)^3 \left(i d (f+g x)^n\right)^{-3/n} \Gamma \left(\frac{3}{n},i d (f+g x)^n\right)}{2 g^3 n}",1,"(a*x^3)/3 + ((I/2)*b*(f + g*x)*(-(f^2*((-I)*d*(f + g*x)^n)^(3/n)*(I*d*(f + g*x)^n)^(2/n)*Gamma[n^(-1), I*d*(f + g*x)^n]) - (f + g*x)*(-2*f*((-I)*d*(f + g*x)^n)^(3/n)*(I*d*(f + g*x)^n)^n^(-1)*Gamma[2/n, I*d*(f + g*x)^n] - (f + g*x)*(-(((-I)*d*(f + g*x)^n)^(3/n)*Gamma[3/n, I*d*(f + g*x)^n]) + (I*d*(f + g*x)^n)^(3/n)*Gamma[3/n, (-I)*d*(f + g*x)^n]*(Cos[c] + I*Sin[c])^2) + 2*f*((-I)*d*(f + g*x)^n)^n^(-1)*(I*d*(f + g*x)^n)^(3/n)*Gamma[2/n, (-I)*d*(f + g*x)^n]*(Cos[c] + I*Sin[c])^2) + f^2*((-I)*d*(f + g*x)^n)^(2/n)*(I*d*(f + g*x)^n)^(3/n)*Gamma[n^(-1), (-I)*d*(f + g*x)^n]*(Cos[c] + I*Sin[c])^2)*(Cos[c] - I*Sin[c]))/(g^3*n*(d^2*(f + g*x)^(2*n))^(3/n))","A",1
268,1,215,255,0.5151171,"\int x \left(a+b \sin \left(c+d (f+g x)^n\right)\right) \, dx","Integrate[x*(a + b*Sin[c + d*(f + g*x)^n]),x]","\frac{a x^2}{2}+\frac{b (\sin (c)-i \cos (c)) (f+g x) \left(-i d (f+g x)^n\right)^{-2/n} \left(f \left(-i d (f+g x)^n\right)^{\frac{1}{n}} \Gamma \left(\frac{1}{n},-i d (f+g x)^n\right)-(f+g x) \Gamma \left(\frac{2}{n},-i d (f+g x)^n\right)\right)}{2 g^2 n}+\frac{b (\sin (c)+i \cos (c)) (f+g x) \left(i d (f+g x)^n\right)^{-2/n} \left(f \left(i d (f+g x)^n\right)^{\frac{1}{n}} \Gamma \left(\frac{1}{n},i d (f+g x)^n\right)-(f+g x) \Gamma \left(\frac{2}{n},i d (f+g x)^n\right)\right)}{2 g^2 n}","\frac{a x^2}{2}+\frac{i b e^{i c} (f+g x)^2 \left(-i d (f+g x)^n\right)^{-2/n} \Gamma \left(\frac{2}{n},-i d (f+g x)^n\right)}{2 g^2 n}-\frac{i b e^{i c} f (f+g x) \left(-i d (f+g x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-i d (f+g x)^n\right)}{2 g^2 n}+\frac{i b e^{-i c} f (f+g x) \left(i d (f+g x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},i d (f+g x)^n\right)}{2 g^2 n}-\frac{i b e^{-i c} (f+g x)^2 \left(i d (f+g x)^n\right)^{-2/n} \Gamma \left(\frac{2}{n},i d (f+g x)^n\right)}{2 g^2 n}",1,"(a*x^2)/2 + (b*(f + g*x)*(f*((-I)*d*(f + g*x)^n)^n^(-1)*Gamma[n^(-1), (-I)*d*(f + g*x)^n] - (f + g*x)*Gamma[2/n, (-I)*d*(f + g*x)^n])*((-I)*Cos[c] + Sin[c]))/(2*g^2*n*((-I)*d*(f + g*x)^n)^(2/n)) + (b*(f + g*x)*(f*(I*d*(f + g*x)^n)^n^(-1)*Gamma[n^(-1), I*d*(f + g*x)^n] - (f + g*x)*Gamma[2/n, I*d*(f + g*x)^n])*(I*Cos[c] + Sin[c]))/(2*g^2*n*(I*d*(f + g*x)^n)^(2/n))","A",1
269,1,126,122,0.2595533,"\int \left(a+b \sin \left(c+d (f+g x)^n\right)\right) \, dx","Integrate[a + b*Sin[c + d*(f + g*x)^n],x]","a x+\frac{i b (\cos (c)+i \sin (c)) (f+g x) \left(-i d (f+g x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-i d (f+g x)^n\right)}{2 g n}-\frac{i b (\cos (c)-i \sin (c)) (f+g x) \left(i d (f+g x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},i d (f+g x)^n\right)}{2 g n}","a x+\frac{i b e^{i c} (f+g x) \left(-i d (f+g x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-i d (f+g x)^n\right)}{2 g n}-\frac{i b e^{-i c} (f+g x) \left(i d (f+g x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},i d (f+g x)^n\right)}{2 g n}",1,"a*x - ((I/2)*b*(f + g*x)*Gamma[n^(-1), I*d*(f + g*x)^n]*(Cos[c] - I*Sin[c]))/(g*n*(I*d*(f + g*x)^n)^n^(-1)) + ((I/2)*b*(f + g*x)*Gamma[n^(-1), (-I)*d*(f + g*x)^n]*(Cos[c] + I*Sin[c]))/(g*n*((-I)*d*(f + g*x)^n)^n^(-1))","A",1
270,0,0,26,3.2816609,"\int \frac{a+b \sin \left(c+d (f+g x)^n\right)}{x} \, dx","Integrate[(a + b*Sin[c + d*(f + g*x)^n])/x,x]","\int \frac{a+b \sin \left(c+d (f+g x)^n\right)}{x} \, dx","b \text{Int}\left(\frac{\sin \left(c+d (f+g x)^n\right)}{x},x\right)+a \log (x)",0,"Integrate[(a + b*Sin[c + d*(f + g*x)^n])/x, x]","A",-1
271,0,0,28,2.8907346,"\int \frac{a+b \sin \left(c+d (f+g x)^n\right)}{x^2} \, dx","Integrate[(a + b*Sin[c + d*(f + g*x)^n])/x^2,x]","\int \frac{a+b \sin \left(c+d (f+g x)^n\right)}{x^2} \, dx","b \text{Int}\left(\frac{\sin \left(c+d (f+g x)^n\right)}{x^2},x\right)-\frac{a}{x}",0,"Integrate[(a + b*Sin[c + d*(f + g*x)^n])/x^2, x]","A",-1
272,1,786,856,26.636002,"\int x^2 \left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2 \, dx","Integrate[x^2*(a + b*Sin[c + d*(f + g*x)^n])^2,x]","\frac{1}{12} \left(4 a^2 x^3-\frac{3 b (f+g x) \left(4 a f^2 (\sin (c)-i \cos (c)) \left(-i d (f+g x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-i d (f+g x)^n\right)+4 a f^2 (\sin (c)+i \cos (c)) \left(i d (f+g x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},i d (f+g x)^n\right)+4 a (\sin (c)-i \cos (c)) (f+g x)^2 \left(-i d (f+g x)^n\right)^{-3/n} \Gamma \left(\frac{3}{n},-i d (f+g x)^n\right)+8 i a f (\cos (c)+i \sin (c)) (f+g x) \left(-i d (f+g x)^n\right)^{-2/n} \Gamma \left(\frac{2}{n},-i d (f+g x)^n\right)-8 i a f (\cos (c)-i \sin (c)) (f+g x) \left(i d (f+g x)^n\right)^{-2/n} \Gamma \left(\frac{2}{n},i d (f+g x)^n\right)+4 a (\sin (c)+i \cos (c)) (f+g x)^2 \left(i d (f+g x)^n\right)^{-3/n} \Gamma \left(\frac{3}{n},i d (f+g x)^n\right)-b f^2 (\cos (c)+i \sin (c))^2 \left(\cosh \left(\frac{\log (2)}{n}\right)-\sinh \left(\frac{\log (2)}{n}\right)\right) \left(-i d (f+g x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-2 i d (f+g x)^n\right)-b f^2 (\cos (c)-i \sin (c))^2 \left(\cosh \left(\frac{\log (2)}{n}\right)-\sinh \left(\frac{\log (2)}{n}\right)\right) \left(i d (f+g x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},2 i d (f+g x)^n\right)-b (\cos (c)+i \sin (c))^2 (f+g x)^2 \left(\cosh \left(\frac{\log (8)}{n}\right)-\sinh \left(\frac{\log (8)}{n}\right)\right) \left(-i d (f+g x)^n\right)^{-3/n} \Gamma \left(\frac{3}{n},-2 i d (f+g x)^n\right)+2 b f (\cos (c)+i \sin (c))^2 (f+g x) \left(\cosh \left(\frac{\log (4)}{n}\right)-\sinh \left(\frac{\log (4)}{n}\right)\right) \left(-i d (f+g x)^n\right)^{-2/n} \Gamma \left(\frac{2}{n},-2 i d (f+g x)^n\right)+2 b f (\cos (c)-i \sin (c))^2 (f+g x) \left(\cosh \left(\frac{\log (4)}{n}\right)-\sinh \left(\frac{\log (4)}{n}\right)\right) \left(i d (f+g x)^n\right)^{-2/n} \Gamma \left(\frac{2}{n},2 i d (f+g x)^n\right)-b (\cos (c)-i \sin (c))^2 (f+g x)^2 \left(\cosh \left(\frac{\log (8)}{n}\right)-\sinh \left(\frac{\log (8)}{n}\right)\right) \left(i d (f+g x)^n\right)^{-3/n} \Gamma \left(\frac{3}{n},2 i d (f+g x)^n\right)\right)}{g^3 n}+2 b^2 x^3\right)","\frac{i a b e^{i c} (f+g x)^3 \Gamma \left(\frac{3}{n},-i d (f+g x)^n\right) \left(-i d (f+g x)^n\right)^{-3/n}}{g^3 n}+\frac{2^{-2-\frac{3}{n}} b^2 e^{2 i c} (f+g x)^3 \Gamma \left(\frac{3}{n},-2 i d (f+g x)^n\right) \left(-i d (f+g x)^n\right)^{-3/n}}{g^3 n}-\frac{2 i a b e^{i c} f (f+g x)^2 \Gamma \left(\frac{2}{n},-i d (f+g x)^n\right) \left(-i d (f+g x)^n\right)^{-2/n}}{g^3 n}-\frac{2^{-1-\frac{2}{n}} b^2 e^{2 i c} f (f+g x)^2 \Gamma \left(\frac{2}{n},-2 i d (f+g x)^n\right) \left(-i d (f+g x)^n\right)^{-2/n}}{g^3 n}+\frac{i a b e^{i c} f^2 (f+g x) \Gamma \left(\frac{1}{n},-i d (f+g x)^n\right) \left(-i d (f+g x)^n\right)^{-1/n}}{g^3 n}+\frac{2^{-2-\frac{1}{n}} b^2 e^{2 i c} f^2 (f+g x) \Gamma \left(\frac{1}{n},-2 i d (f+g x)^n\right) \left(-i d (f+g x)^n\right)^{-1/n}}{g^3 n}+\frac{\left(2 a^2+b^2\right) (f+g x)^3}{6 g^3}-\frac{\left(2 a^2+b^2\right) f (f+g x)^2}{2 g^3}+\frac{\left(2 a^2+b^2\right) f^2 x}{2 g^2}-\frac{i a b e^{-i c} f^2 (f+g x) \left(i d (f+g x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},i d (f+g x)^n\right)}{g^3 n}+\frac{2^{-2-\frac{1}{n}} b^2 e^{-2 i c} f^2 (f+g x) \left(i d (f+g x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},2 i d (f+g x)^n\right)}{g^3 n}+\frac{2 i a b e^{-i c} f (f+g x)^2 \left(i d (f+g x)^n\right)^{-2/n} \Gamma \left(\frac{2}{n},i d (f+g x)^n\right)}{g^3 n}-\frac{2^{-1-\frac{2}{n}} b^2 e^{-2 i c} f (f+g x)^2 \left(i d (f+g x)^n\right)^{-2/n} \Gamma \left(\frac{2}{n},2 i d (f+g x)^n\right)}{g^3 n}-\frac{i a b e^{-i c} (f+g x)^3 \left(i d (f+g x)^n\right)^{-3/n} \Gamma \left(\frac{3}{n},i d (f+g x)^n\right)}{g^3 n}+\frac{2^{-2-\frac{3}{n}} b^2 e^{-2 i c} (f+g x)^3 \left(i d (f+g x)^n\right)^{-3/n} \Gamma \left(\frac{3}{n},2 i d (f+g x)^n\right)}{g^3 n}",1,"(4*a^2*x^3 + 2*b^2*x^3 - (3*b*(f + g*x)*(((-8*I)*a*f*(f + g*x)*Gamma[2/n, I*d*(f + g*x)^n]*(Cos[c] - I*Sin[c]))/(I*d*(f + g*x)^n)^(2/n) + ((8*I)*a*f*(f + g*x)*Gamma[2/n, (-I)*d*(f + g*x)^n]*(Cos[c] + I*Sin[c]))/((-I)*d*(f + g*x)^n)^(2/n) + (4*a*f^2*Gamma[n^(-1), (-I)*d*(f + g*x)^n]*((-I)*Cos[c] + Sin[c]))/((-I)*d*(f + g*x)^n)^n^(-1) + (4*a*(f + g*x)^2*Gamma[3/n, (-I)*d*(f + g*x)^n]*((-I)*Cos[c] + Sin[c]))/((-I)*d*(f + g*x)^n)^(3/n) + (4*a*f^2*Gamma[n^(-1), I*d*(f + g*x)^n]*(I*Cos[c] + Sin[c]))/(I*d*(f + g*x)^n)^n^(-1) + (4*a*(f + g*x)^2*Gamma[3/n, I*d*(f + g*x)^n]*(I*Cos[c] + Sin[c]))/(I*d*(f + g*x)^n)^(3/n) - (b*f^2*Gamma[n^(-1), (2*I)*d*(f + g*x)^n]*(Cos[c] - I*Sin[c])^2*(Cosh[Log[2]/n] - Sinh[Log[2]/n]))/(I*d*(f + g*x)^n)^n^(-1) - (b*f^2*Gamma[n^(-1), (-2*I)*d*(f + g*x)^n]*(Cos[c] + I*Sin[c])^2*(Cosh[Log[2]/n] - Sinh[Log[2]/n]))/((-I)*d*(f + g*x)^n)^n^(-1) + (2*b*f*(f + g*x)*Gamma[2/n, (2*I)*d*(f + g*x)^n]*(Cos[c] - I*Sin[c])^2*(Cosh[Log[4]/n] - Sinh[Log[4]/n]))/(I*d*(f + g*x)^n)^(2/n) + (2*b*f*(f + g*x)*Gamma[2/n, (-2*I)*d*(f + g*x)^n]*(Cos[c] + I*Sin[c])^2*(Cosh[Log[4]/n] - Sinh[Log[4]/n]))/((-I)*d*(f + g*x)^n)^(2/n) - (b*(f + g*x)^2*Gamma[3/n, (2*I)*d*(f + g*x)^n]*(Cos[c] - I*Sin[c])^2*(Cosh[Log[8]/n] - Sinh[Log[8]/n]))/(I*d*(f + g*x)^n)^(3/n) - (b*(f + g*x)^2*Gamma[3/n, (-2*I)*d*(f + g*x)^n]*(Cos[c] + I*Sin[c])^2*(Cosh[Log[8]/n] - Sinh[Log[8]/n]))/((-I)*d*(f + g*x)^n)^(3/n)))/(g^3*n))/12","A",0
273,1,552,556,16.5735752,"\int x \left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2 \, dx","Integrate[x*(a + b*Sin[c + d*(f + g*x)^n])^2,x]","\frac{2 a^2 g^2 n x^2+4 i a b (\cos (c)+i \sin (c)) (f+g x)^2 \left(-i d (f+g x)^n\right)^{-2/n} \Gamma \left(\frac{2}{n},-i d (f+g x)^n\right)+4 a b f (\sin (c)-i \cos (c)) (f+g x) \left(-i d (f+g x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-i d (f+g x)^n\right)-4 i a b (\cos (c)-i \sin (c)) (f+g x)^2 \left(i d (f+g x)^n\right)^{-2/n} \Gamma \left(\frac{2}{n},i d (f+g x)^n\right)+4 a b f (\sin (c)+i \cos (c)) (f+g x) \left(i d (f+g x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},i d (f+g x)^n\right)+b^2 (\cos (c)+i \sin (c))^2 (f+g x)^2 \left(\cosh \left(\frac{\log (4)}{n}\right)-\sinh \left(\frac{\log (4)}{n}\right)\right) \left(-i d (f+g x)^n\right)^{-2/n} \Gamma \left(\frac{2}{n},-2 i d (f+g x)^n\right)-b^2 f (\cos (c)+i \sin (c))^2 (f+g x) \left(\cosh \left(\frac{\log (2)}{n}\right)-\sinh \left(\frac{\log (2)}{n}\right)\right) \left(-i d (f+g x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-2 i d (f+g x)^n\right)-b^2 f (\cos (c)-i \sin (c))^2 (f+g x) \left(\cosh \left(\frac{\log (2)}{n}\right)-\sinh \left(\frac{\log (2)}{n}\right)\right) \left(i d (f+g x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},2 i d (f+g x)^n\right)+b^2 (\cos (c)-i \sin (c))^2 (f+g x)^2 \left(\cosh \left(\frac{\log (4)}{n}\right)-\sinh \left(\frac{\log (4)}{n}\right)\right) \left(i d (f+g x)^n\right)^{-2/n} \Gamma \left(\frac{2}{n},2 i d (f+g x)^n\right)+b^2 g^2 n x^2}{4 g^2 n}","\frac{\left(2 a^2+b^2\right) (f+g x)^2}{4 g^2}-\frac{f x \left(2 a^2+b^2\right)}{2 g}+\frac{i a b e^{i c} (f+g x)^2 \left(-i d (f+g x)^n\right)^{-2/n} \Gamma \left(\frac{2}{n},-i d (f+g x)^n\right)}{g^2 n}-\frac{i a b e^{i c} f (f+g x) \left(-i d (f+g x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-i d (f+g x)^n\right)}{g^2 n}+\frac{i a b e^{-i c} f (f+g x) \left(i d (f+g x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},i d (f+g x)^n\right)}{g^2 n}-\frac{i a b e^{-i c} (f+g x)^2 \left(i d (f+g x)^n\right)^{-2/n} \Gamma \left(\frac{2}{n},i d (f+g x)^n\right)}{g^2 n}+\frac{b^2 e^{2 i c} 4^{-\frac{1}{n}-1} (f+g x)^2 \left(-i d (f+g x)^n\right)^{-2/n} \Gamma \left(\frac{2}{n},-2 i d (f+g x)^n\right)}{g^2 n}-\frac{b^2 e^{2 i c} f 2^{-\frac{1}{n}-2} (f+g x) \left(-i d (f+g x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-2 i d (f+g x)^n\right)}{g^2 n}-\frac{b^2 e^{-2 i c} f 2^{-\frac{1}{n}-2} (f+g x) \left(i d (f+g x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},2 i d (f+g x)^n\right)}{g^2 n}+\frac{b^2 e^{-2 i c} 4^{-\frac{1}{n}-1} (f+g x)^2 \left(i d (f+g x)^n\right)^{-2/n} \Gamma \left(\frac{2}{n},2 i d (f+g x)^n\right)}{g^2 n}",1,"(2*a^2*g^2*n*x^2 + b^2*g^2*n*x^2 - ((4*I)*a*b*(f + g*x)^2*Gamma[2/n, I*d*(f + g*x)^n]*(Cos[c] - I*Sin[c]))/(I*d*(f + g*x)^n)^(2/n) + ((4*I)*a*b*(f + g*x)^2*Gamma[2/n, (-I)*d*(f + g*x)^n]*(Cos[c] + I*Sin[c]))/((-I)*d*(f + g*x)^n)^(2/n) + (4*a*b*f*(f + g*x)*Gamma[n^(-1), (-I)*d*(f + g*x)^n]*((-I)*Cos[c] + Sin[c]))/((-I)*d*(f + g*x)^n)^n^(-1) + (4*a*b*f*(f + g*x)*Gamma[n^(-1), I*d*(f + g*x)^n]*(I*Cos[c] + Sin[c]))/(I*d*(f + g*x)^n)^n^(-1) - (b^2*f*(f + g*x)*Gamma[n^(-1), (2*I)*d*(f + g*x)^n]*(Cos[c] - I*Sin[c])^2*(Cosh[Log[2]/n] - Sinh[Log[2]/n]))/(I*d*(f + g*x)^n)^n^(-1) - (b^2*f*(f + g*x)*Gamma[n^(-1), (-2*I)*d*(f + g*x)^n]*(Cos[c] + I*Sin[c])^2*(Cosh[Log[2]/n] - Sinh[Log[2]/n]))/((-I)*d*(f + g*x)^n)^n^(-1) + (b^2*(f + g*x)^2*Gamma[2/n, (2*I)*d*(f + g*x)^n]*(Cos[c] - I*Sin[c])^2*(Cosh[Log[4]/n] - Sinh[Log[4]/n]))/(I*d*(f + g*x)^n)^(2/n) + (b^2*(f + g*x)^2*Gamma[2/n, (-2*I)*d*(f + g*x)^n]*(Cos[c] + I*Sin[c])^2*(Cosh[Log[4]/n] - Sinh[Log[4]/n]))/((-I)*d*(f + g*x)^n)^(2/n))/(4*g^2*n)","A",0
274,1,381,261,1.7344444,"\int \left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2 \, dx","Integrate[(a + b*Sin[c + d*(f + g*x)^n])^2,x]","\frac{4 a^2 g n x-4 i a b e^{-i c} (f+g x) \left(i d (f+g x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},i d (f+g x)^n\right)+4 i a b (\cos (c)+i \sin (c)) (f+g x) \left(-i d (f+g x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-i d (f+g x)^n\right)+b^2 e^{2 i c} f 2^{-1/n} \left(i d (f+g x)^n\right)^{\frac{1}{n}} \left(d^2 (f+g x)^{2 n}\right)^{-1/n} \Gamma \left(\frac{1}{n},-2 i d (f+g x)^n\right)+b^2 e^{2 i c} g 2^{-1/n} x \left(i d (f+g x)^n\right)^{\frac{1}{n}} \left(d^2 (f+g x)^{2 n}\right)^{-1/n} \Gamma \left(\frac{1}{n},-2 i d (f+g x)^n\right)+b^2 e^{-2 i c} f 2^{-1/n} \left(i d (f+g x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},2 i d (f+g x)^n\right)+b^2 e^{-2 i c} g 2^{-1/n} x \left(i d (f+g x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},2 i d (f+g x)^n\right)+2 b^2 g n x}{4 g n}","\frac{1}{2} x \left(2 a^2+b^2\right)+\frac{i a b e^{i c} (f+g x) \left(-i d (f+g x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-i d (f+g x)^n\right)}{g n}-\frac{i a b e^{-i c} (f+g x) \left(i d (f+g x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},i d (f+g x)^n\right)}{g n}+\frac{b^2 e^{2 i c} 2^{-\frac{1}{n}-2} (f+g x) \left(-i d (f+g x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-2 i d (f+g x)^n\right)}{g n}+\frac{b^2 e^{-2 i c} 2^{-\frac{1}{n}-2} (f+g x) \left(i d (f+g x)^n\right)^{-1/n} \Gamma \left(\frac{1}{n},2 i d (f+g x)^n\right)}{g n}",1,"(4*a^2*g*n*x + 2*b^2*g*n*x - ((4*I)*a*b*(f + g*x)*Gamma[n^(-1), I*d*(f + g*x)^n])/(E^(I*c)*(I*d*(f + g*x)^n)^n^(-1)) + (b^2*E^((2*I)*c)*f*(I*d*(f + g*x)^n)^n^(-1)*Gamma[n^(-1), (-2*I)*d*(f + g*x)^n])/(2^n^(-1)*(d^2*(f + g*x)^(2*n))^n^(-1)) + (b^2*E^((2*I)*c)*g*x*(I*d*(f + g*x)^n)^n^(-1)*Gamma[n^(-1), (-2*I)*d*(f + g*x)^n])/(2^n^(-1)*(d^2*(f + g*x)^(2*n))^n^(-1)) + (b^2*f*Gamma[n^(-1), (2*I)*d*(f + g*x)^n])/(2^n^(-1)*E^((2*I)*c)*(I*d*(f + g*x)^n)^n^(-1)) + (b^2*g*x*Gamma[n^(-1), (2*I)*d*(f + g*x)^n])/(2^n^(-1)*E^((2*I)*c)*(I*d*(f + g*x)^n)^n^(-1)) + ((4*I)*a*b*(f + g*x)*Gamma[n^(-1), (-I)*d*(f + g*x)^n]*(Cos[c] + I*Sin[c]))/((-I)*d*(f + g*x)^n)^n^(-1))/(4*g*n)","A",1
275,0,0,25,3.9391046,"\int \frac{\left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2}{x} \, dx","Integrate[(a + b*Sin[c + d*(f + g*x)^n])^2/x,x]","\int \frac{\left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2}{x} \, dx","\text{Int}\left(\frac{\left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2}{x},x\right)",0,"Integrate[(a + b*Sin[c + d*(f + g*x)^n])^2/x, x]","A",-1
276,0,0,25,3.3404561,"\int \frac{\left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2}{x^2} \, dx","Integrate[(a + b*Sin[c + d*(f + g*x)^n])^2/x^2,x]","\int \frac{\left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2}{x^2} \, dx","\text{Int}\left(\frac{\left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2}{x^2},x\right)",0,"Integrate[(a + b*Sin[c + d*(f + g*x)^n])^2/x^2, x]","A",-1
277,0,0,25,1.5058391,"\int \frac{x^2}{a+b \sin \left(c+d (f+g x)^n\right)} \, dx","Integrate[x^2/(a + b*Sin[c + d*(f + g*x)^n]),x]","\int \frac{x^2}{a+b \sin \left(c+d (f+g x)^n\right)} \, dx","\text{Int}\left(\frac{x^2}{a+b \sin \left(c+d (f+g x)^n\right)},x\right)",0,"Integrate[x^2/(a + b*Sin[c + d*(f + g*x)^n]), x]","A",-1
278,0,0,23,1.321288,"\int \frac{x}{a+b \sin \left(c+d (f+g x)^n\right)} \, dx","Integrate[x/(a + b*Sin[c + d*(f + g*x)^n]),x]","\int \frac{x}{a+b \sin \left(c+d (f+g x)^n\right)} \, dx","\text{Int}\left(\frac{x}{a+b \sin \left(c+d (f+g x)^n\right)},x\right)",0,"Integrate[x/(a + b*Sin[c + d*(f + g*x)^n]), x]","A",-1
279,0,0,21,0.2778233,"\int \frac{1}{a+b \sin \left(c+d (f+g x)^n\right)} \, dx","Integrate[(a + b*Sin[c + d*(f + g*x)^n])^(-1),x]","\int \frac{1}{a+b \sin \left(c+d (f+g x)^n\right)} \, dx","\text{Int}\left(\frac{1}{a+b \sin \left(c+d (f+g x)^n\right)},x\right)",0,"Integrate[(a + b*Sin[c + d*(f + g*x)^n])^(-1), x]","A",-1
280,0,0,25,0.7265679,"\int \frac{1}{x \left(a+b \sin \left(c+d (f+g x)^n\right)\right)} \, dx","Integrate[1/(x*(a + b*Sin[c + d*(f + g*x)^n])),x]","\int \frac{1}{x \left(a+b \sin \left(c+d (f+g x)^n\right)\right)} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \sin \left(c+d (f+g x)^n\right)\right)},x\right)",0,"Integrate[1/(x*(a + b*Sin[c + d*(f + g*x)^n])), x]","A",-1
281,0,0,25,0.837343,"\int \frac{1}{x^2 \left(a+b \sin \left(c+d (f+g x)^n\right)\right)} \, dx","Integrate[1/(x^2*(a + b*Sin[c + d*(f + g*x)^n])),x]","\int \frac{1}{x^2 \left(a+b \sin \left(c+d (f+g x)^n\right)\right)} \, dx","\text{Int}\left(\frac{1}{x^2 \left(a+b \sin \left(c+d (f+g x)^n\right)\right)},x\right)",0,"Integrate[1/(x^2*(a + b*Sin[c + d*(f + g*x)^n])), x]","A",-1
282,-1,0,25,180.1198805,"\int \frac{x^2}{\left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2} \, dx","Integrate[x^2/(a + b*Sin[c + d*(f + g*x)^n])^2,x]","\text{\$Aborted}","\text{Int}\left(\frac{x^2}{\left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2},x\right)",0,"$Aborted","F",-1
283,-1,0,23,180.0844472,"\int \frac{x}{\left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2} \, dx","Integrate[x/(a + b*Sin[c + d*(f + g*x)^n])^2,x]","\text{\$Aborted}","\text{Int}\left(\frac{x}{\left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2},x\right)",0,"$Aborted","F",-1
284,0,0,21,11.5786312,"\int \frac{1}{\left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2} \, dx","Integrate[(a + b*Sin[c + d*(f + g*x)^n])^(-2),x]","\int \frac{1}{\left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{\left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2},x\right)",0,"Integrate[(a + b*Sin[c + d*(f + g*x)^n])^(-2), x]","A",-1
285,-1,0,25,180.0800974,"\int \frac{1}{x \left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2} \, dx","Integrate[1/(x*(a + b*Sin[c + d*(f + g*x)^n])^2),x]","\text{\$Aborted}","\text{Int}\left(\frac{1}{x \left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2},x\right)",0,"$Aborted","F",-1
286,-1,0,25,180.123866,"\int \frac{1}{x^2 \left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2} \, dx","Integrate[1/(x^2*(a + b*Sin[c + d*(f + g*x)^n])^2),x]","\text{\$Aborted}","\text{Int}\left(\frac{1}{x^2 \left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2},x\right)",0,"$Aborted","F",-1
287,0,0,27,2.1075932,"\int (e x)^m \left(a+b \sin \left(c+d (f+g x)^n\right)\right)^p \, dx","Integrate[(e*x)^m*(a + b*Sin[c + d*(f + g*x)^n])^p,x]","\int (e x)^m \left(a+b \sin \left(c+d (f+g x)^n\right)\right)^p \, dx","\text{Int}\left((e x)^m \left(a+b \sin \left(c+d (f+g x)^n\right)\right)^p,x\right)",0,"Integrate[(e*x)^m*(a + b*Sin[c + d*(f + g*x)^n])^p, x]","A",-1
288,1,150,224,0.6219412,"\int (e+f x)^2 \left(a+b \sin \left(c+\frac{d}{x}\right)\right) \, dx","Integrate[(e + f*x)^2*(a + b*Sin[c + d/x]),x]","\frac{1}{6} \left(x \left(2 a \left(3 e^2+3 e f x+f^2 x^2\right)+b \sin \left(c+\frac{d}{x}\right) \left(-f^2 \left(d^2-2 x^2\right)+6 e^2+6 e f x\right)+b d f (6 e+f x) \cos \left(c+\frac{d}{x}\right)\right)+b d \text{Ci}\left(\frac{d}{x}\right) \left(\cos (c) \left(d^2 f^2-6 e^2\right)+6 d e f \sin (c)\right)-b d \text{Si}\left(\frac{d}{x}\right) \left(\sin (c) \left(d^2 f^2-6 e^2\right)-6 d e f \cos (c)\right)\right)","a e^2 x+a e f x^2+\frac{1}{3} a f^2 x^3+\frac{1}{6} b d^3 f^2 \cos (c) \text{Ci}\left(\frac{d}{x}\right)+b d^2 e f \sin (c) \text{Ci}\left(\frac{d}{x}\right)-b d e^2 \cos (c) \text{Ci}\left(\frac{d}{x}\right)-\frac{1}{6} b d^3 f^2 \sin (c) \text{Si}\left(\frac{d}{x}\right)+b d^2 e f \cos (c) \text{Si}\left(\frac{d}{x}\right)-\frac{1}{6} b d^2 f^2 x \sin \left(c+\frac{d}{x}\right)+b d e^2 \sin (c) \text{Si}\left(\frac{d}{x}\right)+b e^2 x \sin \left(c+\frac{d}{x}\right)+b e f x^2 \sin \left(c+\frac{d}{x}\right)+b d e f x \cos \left(c+\frac{d}{x}\right)+\frac{1}{3} b f^2 x^3 \sin \left(c+\frac{d}{x}\right)+\frac{1}{6} b d f^2 x^2 \cos \left(c+\frac{d}{x}\right)",1,"(b*d*CosIntegral[d/x]*((-6*e^2 + d^2*f^2)*Cos[c] + 6*d*e*f*Sin[c]) + x*(2*a*(3*e^2 + 3*e*f*x + f^2*x^2) + b*d*f*(6*e + f*x)*Cos[c + d/x] + b*(6*e^2 + 6*e*f*x - f^2*(d^2 - 2*x^2))*Sin[c + d/x]) - b*d*(-6*d*e*f*Cos[c] + (-6*e^2 + d^2*f^2)*Sin[c])*SinIntegral[d/x])/6","A",1
289,1,79,118,0.2334786,"\int (e+f x) \left(a+b \sin \left(c+\frac{d}{x}\right)\right) \, dx","Integrate[(e + f*x)*(a + b*Sin[c + d/x]),x]","\frac{1}{2} \left(x (2 e+f x) \left(a+b \sin \left(c+\frac{d}{x}\right)\right)+b d \text{Ci}\left(\frac{d}{x}\right) (d f \sin (c)-2 e \cos (c))+b d \text{Si}\left(\frac{d}{x}\right) (d f \cos (c)+2 e \sin (c))+b d f x \cos \left(c+\frac{d}{x}\right)\right)","a e x+\frac{1}{2} a f x^2+\frac{1}{2} b d^2 f \sin (c) \text{Ci}\left(\frac{d}{x}\right)-b d e \cos (c) \text{Ci}\left(\frac{d}{x}\right)+\frac{1}{2} b d^2 f \cos (c) \text{Si}\left(\frac{d}{x}\right)+b d e \sin (c) \text{Si}\left(\frac{d}{x}\right)+b e x \sin \left(c+\frac{d}{x}\right)+\frac{1}{2} b f x^2 \sin \left(c+\frac{d}{x}\right)+\frac{1}{2} b d f x \cos \left(c+\frac{d}{x}\right)",1,"(b*d*f*x*Cos[c + d/x] + b*d*CosIntegral[d/x]*(-2*e*Cos[c] + d*f*Sin[c]) + x*(2*e + f*x)*(a + b*Sin[c + d/x]) + b*d*(d*f*Cos[c] + 2*e*Sin[c])*SinIntegral[d/x])/2","A",1
290,1,50,38,0.0331511,"\int \left(a+b \sin \left(c+\frac{d}{x}\right)\right) \, dx","Integrate[a + b*Sin[c + d/x],x]","a x-b d \left(\cos (c) \text{Ci}\left(\frac{d}{x}\right)-\sin (c) \text{Si}\left(\frac{d}{x}\right)\right)+b x \sin (c) \cos \left(\frac{d}{x}\right)+b x \cos (c) \sin \left(\frac{d}{x}\right)","a x-b d \cos (c) \text{Ci}\left(\frac{d}{x}\right)+b d \sin (c) \text{Si}\left(\frac{d}{x}\right)+b x \sin \left(c+\frac{d}{x}\right)",1,"a*x + b*x*Cos[d/x]*Sin[c] + b*x*Cos[c]*Sin[d/x] - b*d*(Cos[c]*CosIntegral[d/x] - Sin[c]*SinIntegral[d/x])","A",1
291,1,83,103,0.2098071,"\int \frac{a+b \sin \left(c+\frac{d}{x}\right)}{e+f x} \, dx","Integrate[(a + b*Sin[c + d/x])/(e + f*x),x]","\frac{a \log (e+f x)+b \sin \left(c-\frac{d f}{e}\right) \text{Ci}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right)-b \sin (c) \text{Ci}\left(\frac{d}{x}\right)+b \cos \left(c-\frac{d f}{e}\right) \text{Si}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right)-b \cos (c) \text{Si}\left(\frac{d}{x}\right)}{f}","\frac{a \log \left(\frac{e}{x}+f\right)}{f}+\frac{a \log (x)}{f}+\frac{b \sin \left(c-\frac{d f}{e}\right) \text{Ci}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right)}{f}-\frac{b \sin (c) \text{Ci}\left(\frac{d}{x}\right)}{f}+\frac{b \cos \left(c-\frac{d f}{e}\right) \text{Si}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right)}{f}-\frac{b \cos (c) \text{Si}\left(\frac{d}{x}\right)}{f}",1,"(a*Log[e + f*x] - b*CosIntegral[d/x]*Sin[c] + b*CosIntegral[d*(f/e + x^(-1))]*Sin[c - (d*f)/e] + b*Cos[c - (d*f)/e]*SinIntegral[d*(f/e + x^(-1))] - b*Cos[c]*SinIntegral[d/x])/f","A",0
292,1,85,94,0.7430085,"\int \frac{a+b \sin \left(c+\frac{d}{x}\right)}{(e+f x)^2} \, dx","Integrate[(a + b*Sin[c + d/x])/(e + f*x)^2,x]","\frac{\frac{e \left(b f x \sin \left(c+\frac{d}{x}\right)-a e\right)}{f (e+f x)}-b d \cos \left(c-\frac{d f}{e}\right) \text{Ci}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right)+b d \sin \left(c-\frac{d f}{e}\right) \text{Si}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right)}{e^2}","\frac{a}{e \left(\frac{e}{x}+f\right)}-\frac{b d \cos \left(c-\frac{d f}{e}\right) \text{Ci}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right)}{e^2}+\frac{b d \sin \left(c-\frac{d f}{e}\right) \text{Si}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right)}{e^2}+\frac{b \sin \left(c+\frac{d}{x}\right)}{e \left(\frac{e}{x}+f\right)}",1,"(-(b*d*Cos[c - (d*f)/e]*CosIntegral[d*(f/e + x^(-1))]) + (e*(-(a*e) + b*f*x*Sin[c + d/x]))/(f*(e + f*x)) + b*d*Sin[c - (d*f)/e]*SinIntegral[d*(f/e + x^(-1))])/e^2","A",1
293,1,151,233,1.8940523,"\int \frac{a+b \sin \left(c+\frac{d}{x}\right)}{(e+f x)^3} \, dx","Integrate[(a + b*Sin[c + d/x])/(e + f*x)^3,x]","-\frac{\frac{e \left(a e^3+b d f^2 x (e+f x) \cos \left(c+\frac{d}{x}\right)-b e f x (2 e+f x) \sin \left(c+\frac{d}{x}\right)\right)}{f (e+f x)^2}+b d \text{Ci}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right) \left(d f \sin \left(c-\frac{d f}{e}\right)+2 e \cos \left(c-\frac{d f}{e}\right)\right)+b d \text{Si}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right) \left(d f \cos \left(c-\frac{d f}{e}\right)-2 e \sin \left(c-\frac{d f}{e}\right)\right)}{2 e^4}","\frac{a}{e^2 \left(\frac{e}{x}+f\right)}-\frac{a f}{2 e^2 \left(\frac{e}{x}+f\right)^2}-\frac{b d^2 f \sin \left(c-\frac{d f}{e}\right) \text{Ci}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right)}{2 e^4}-\frac{b d \cos \left(c-\frac{d f}{e}\right) \text{Ci}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right)}{e^3}-\frac{b d^2 f \cos \left(c-\frac{d f}{e}\right) \text{Si}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right)}{2 e^4}+\frac{b d \sin \left(c-\frac{d f}{e}\right) \text{Si}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right)}{e^3}-\frac{b d f \cos \left(c+\frac{d}{x}\right)}{2 e^3 \left(\frac{e}{x}+f\right)}+\frac{b \sin \left(c+\frac{d}{x}\right)}{e^2 \left(\frac{e}{x}+f\right)}-\frac{b f \sin \left(c+\frac{d}{x}\right)}{2 e^2 \left(\frac{e}{x}+f\right)^2}",1,"-1/2*(b*d*CosIntegral[d*(f/e + x^(-1))]*(2*e*Cos[c - (d*f)/e] + d*f*Sin[c - (d*f)/e]) + (e*(a*e^3 + b*d*f^2*x*(e + f*x)*Cos[c + d/x] - b*e*f*x*(2*e + f*x)*Sin[c + d/x]))/(f*(e + f*x)^2) + b*d*(d*f*Cos[c - (d*f)/e] - 2*e*Sin[c - (d*f)/e])*SinIntegral[d*(f/e + x^(-1))])/e^4","A",1
294,1,252,254,0.5643276,"\int (e+f x) \left(a+b \sin \left(c+\frac{d}{x}\right)\right)^2 \, dx","Integrate[(e + f*x)*(a + b*Sin[c + d/x])^2,x]","\frac{1}{4} \left(4 a^2 e x+2 a^2 f x^2+4 a b d \text{Ci}\left(\frac{d}{x}\right) (d f \sin (c)-2 e \cos (c))+4 a b d^2 f \cos (c) \text{Si}\left(\frac{d}{x}\right)+8 a b d e \sin (c) \text{Si}\left(\frac{d}{x}\right)+8 a b e x \sin \left(c+\frac{d}{x}\right)+4 a b f x^2 \sin \left(c+\frac{d}{x}\right)+4 a b d f x \cos \left(c+\frac{d}{x}\right)-4 b^2 d \text{Ci}\left(\frac{2 d}{x}\right) (d f \cos (2 c)+e \sin (2 c))+4 b^2 d^2 f \sin (2 c) \text{Si}\left(\frac{2 d}{x}\right)-4 b^2 d e \cos (2 c) \text{Si}\left(\frac{2 d}{x}\right)-2 b^2 e x \cos \left(2 \left(c+\frac{d}{x}\right)\right)-b^2 f x^2 \cos \left(2 \left(c+\frac{d}{x}\right)\right)+2 b^2 d f x \sin \left(2 \left(c+\frac{d}{x}\right)\right)+2 b^2 e x+b^2 f x^2\right)","a^2 e x+\frac{1}{2} a^2 f x^2+a b d^2 f \sin (c) \text{Ci}\left(\frac{d}{x}\right)-2 a b d e \cos (c) \text{Ci}\left(\frac{d}{x}\right)+a b d^2 f \cos (c) \text{Si}\left(\frac{d}{x}\right)+2 a b d e \sin (c) \text{Si}\left(\frac{d}{x}\right)+2 a b e x \sin \left(c+\frac{d}{x}\right)+a b f x^2 \sin \left(c+\frac{d}{x}\right)+a b d f x \cos \left(c+\frac{d}{x}\right)-b^2 d^2 f \cos (2 c) \text{Ci}\left(\frac{2 d}{x}\right)-b^2 d e \sin (2 c) \text{Ci}\left(\frac{2 d}{x}\right)+b^2 d^2 f \sin (2 c) \text{Si}\left(\frac{2 d}{x}\right)-b^2 d e \cos (2 c) \text{Si}\left(\frac{2 d}{x}\right)+b^2 e x \sin ^2\left(c+\frac{d}{x}\right)+\frac{1}{2} b^2 f x^2 \sin ^2\left(c+\frac{d}{x}\right)+b^2 d f x \sin \left(c+\frac{d}{x}\right) \cos \left(c+\frac{d}{x}\right)",1,"(4*a^2*e*x + 2*b^2*e*x + 2*a^2*f*x^2 + b^2*f*x^2 + 4*a*b*d*f*x*Cos[c + d/x] - 2*b^2*e*x*Cos[2*(c + d/x)] - b^2*f*x^2*Cos[2*(c + d/x)] + 4*a*b*d*CosIntegral[d/x]*(-2*e*Cos[c] + d*f*Sin[c]) - 4*b^2*d*CosIntegral[(2*d)/x]*(d*f*Cos[2*c] + e*Sin[2*c]) + 8*a*b*e*x*Sin[c + d/x] + 4*a*b*f*x^2*Sin[c + d/x] + 2*b^2*d*f*x*Sin[2*(c + d/x)] + 4*a*b*d^2*f*Cos[c]*SinIntegral[d/x] + 8*a*b*d*e*Sin[c]*SinIntegral[d/x] - 4*b^2*d*e*Cos[2*c]*SinIntegral[(2*d)/x] + 4*b^2*d^2*f*Sin[2*c]*SinIntegral[(2*d)/x])/4","A",1
295,1,105,94,0.1462333,"\int \left(a+b \sin \left(c+\frac{d}{x}\right)\right)^2 \, dx","Integrate[(a + b*Sin[c + d/x])^2,x]","\frac{1}{2} \left(2 a^2 x-4 a b d \cos (c) \text{Ci}\left(\frac{d}{x}\right)+4 a b d \sin (c) \text{Si}\left(\frac{d}{x}\right)+4 a b x \sin \left(c+\frac{d}{x}\right)-2 b^2 d \sin (2 c) \text{Ci}\left(\frac{2 d}{x}\right)-2 b^2 d \cos (2 c) \text{Si}\left(\frac{2 d}{x}\right)-b^2 x \cos \left(2 \left(c+\frac{d}{x}\right)\right)+b^2 x\right)","a^2 x-2 a b d \cos (c) \text{Ci}\left(\frac{d}{x}\right)+2 a b d \sin (c) \text{Si}\left(\frac{d}{x}\right)+2 a b x \sin \left(c+\frac{d}{x}\right)-b^2 d \sin (2 c) \text{Ci}\left(\frac{2 d}{x}\right)-b^2 d \cos (2 c) \text{Si}\left(\frac{2 d}{x}\right)+b^2 x \sin ^2\left(c+\frac{d}{x}\right)",1,"(2*a^2*x + b^2*x - b^2*x*Cos[2*(c + d/x)] - 4*a*b*d*Cos[c]*CosIntegral[d/x] - 2*b^2*d*CosIntegral[(2*d)/x]*Sin[2*c] + 4*a*b*x*Sin[c + d/x] + 4*a*b*d*Sin[c]*SinIntegral[d/x] - 2*b^2*d*Cos[2*c]*SinIntegral[(2*d)/x])/2","A",1
296,1,195,255,0.4106546,"\int \frac{\left(a+b \sin \left(c+\frac{d}{x}\right)\right)^2}{e+f x} \, dx","Integrate[(a + b*Sin[c + d/x])^2/(e + f*x),x]","\frac{2 a^2 \log (e+f x)+4 a b \sin \left(c-\frac{d f}{e}\right) \text{Ci}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right)-4 a b \sin (c) \text{Ci}\left(\frac{d}{x}\right)+4 a b \cos \left(c-\frac{d f}{e}\right) \text{Si}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right)-4 a b \cos (c) \text{Si}\left(\frac{d}{x}\right)-b^2 \cos \left(2 c-\frac{2 d f}{e}\right) \text{Ci}\left(2 d \left(\frac{f}{e}+\frac{1}{x}\right)\right)+b^2 \cos (2 c) \text{Ci}\left(\frac{2 d}{x}\right)+b^2 \sin \left(2 c-\frac{2 d f}{e}\right) \text{Si}\left(2 d \left(\frac{f}{e}+\frac{1}{x}\right)\right)-b^2 \sin (2 c) \text{Si}\left(\frac{2 d}{x}\right)+b^2 \log (e+f x)}{2 f}","\frac{a^2 \log \left(\frac{e}{x}+f\right)}{f}+\frac{a^2 \log (x)}{f}+\frac{2 a b \sin \left(c-\frac{d f}{e}\right) \text{Ci}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right)}{f}-\frac{2 a b \sin (c) \text{Ci}\left(\frac{d}{x}\right)}{f}+\frac{2 a b \cos \left(c-\frac{d f}{e}\right) \text{Si}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right)}{f}-\frac{2 a b \cos (c) \text{Si}\left(\frac{d}{x}\right)}{f}-\frac{b^2 \cos \left(2 c-\frac{2 d f}{e}\right) \text{Ci}\left(2 d \left(\frac{f}{e}+\frac{1}{x}\right)\right)}{2 f}+\frac{b^2 \cos (2 c) \text{Ci}\left(\frac{2 d}{x}\right)}{2 f}+\frac{b^2 \sin \left(2 c-\frac{2 d f}{e}\right) \text{Si}\left(2 d \left(\frac{f}{e}+\frac{1}{x}\right)\right)}{2 f}-\frac{b^2 \sin (2 c) \text{Si}\left(\frac{2 d}{x}\right)}{2 f}+\frac{b^2 \log \left(\frac{e}{x}+f\right)}{2 f}+\frac{b^2 \log (x)}{2 f}",1,"(-(b^2*Cos[2*c - (2*d*f)/e]*CosIntegral[2*d*(f/e + x^(-1))]) + b^2*Cos[2*c]*CosIntegral[(2*d)/x] + 2*a^2*Log[e + f*x] + b^2*Log[e + f*x] - 4*a*b*CosIntegral[d/x]*Sin[c] + 4*a*b*CosIntegral[d*(f/e + x^(-1))]*Sin[c - (d*f)/e] + 4*a*b*Cos[c - (d*f)/e]*SinIntegral[d*(f/e + x^(-1))] + b^2*Sin[2*c - (2*d*f)/e]*SinIntegral[2*d*(f/e + x^(-1))] - 4*a*b*Cos[c]*SinIntegral[d/x] - b^2*Sin[2*c]*SinIntegral[(2*d)/x])/(2*f)","A",0
297,1,263,195,1.4925507,"\int \frac{\left(a+b \sin \left(c+\frac{d}{x}\right)\right)^2}{(e+f x)^2} \, dx","Integrate[(a + b*Sin[c + d/x])^2/(e + f*x)^2,x]","-\frac{2 a^2 e^2+4 a b d f (e+f x) \cos \left(c-\frac{d f}{e}\right) \text{Ci}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right)-4 a b d f^2 x \sin \left(c-\frac{d f}{e}\right) \text{Si}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right)-4 a b d e f \sin \left(c-\frac{d f}{e}\right) \text{Si}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right)-4 a b e f x \sin \left(c+\frac{d}{x}\right)+2 b^2 d f (e+f x) \sin \left(2 c-\frac{2 d f}{e}\right) \text{Ci}\left(2 d \left(\frac{f}{e}+\frac{1}{x}\right)\right)+2 b^2 d f^2 x \cos \left(2 c-\frac{2 d f}{e}\right) \text{Si}\left(2 d \left(\frac{f}{e}+\frac{1}{x}\right)\right)+2 b^2 d e f \cos \left(2 c-\frac{2 d f}{e}\right) \text{Si}\left(2 d \left(\frac{f}{e}+\frac{1}{x}\right)\right)+b^2 e f x \cos \left(2 \left(c+\frac{d}{x}\right)\right)+b^2 e^2}{2 e^2 f (e+f x)}","\frac{a^2}{e \left(\frac{e}{x}+f\right)}-\frac{2 a b d \cos \left(c-\frac{d f}{e}\right) \text{Ci}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right)}{e^2}+\frac{2 a b d \sin \left(c-\frac{d f}{e}\right) \text{Si}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right)}{e^2}+\frac{2 a b \sin \left(c+\frac{d}{x}\right)}{e \left(\frac{e}{x}+f\right)}-\frac{b^2 d \sin \left(2 c-\frac{2 d f}{e}\right) \text{Ci}\left(2 d \left(\frac{f}{e}+\frac{1}{x}\right)\right)}{e^2}-\frac{b^2 d \cos \left(2 c-\frac{2 d f}{e}\right) \text{Si}\left(2 d \left(\frac{f}{e}+\frac{1}{x}\right)\right)}{e^2}+\frac{b^2 \sin ^2\left(c+\frac{d}{x}\right)}{e \left(\frac{e}{x}+f\right)}",1,"-1/2*(2*a^2*e^2 + b^2*e^2 + b^2*e*f*x*Cos[2*(c + d/x)] + 4*a*b*d*f*(e + f*x)*Cos[c - (d*f)/e]*CosIntegral[d*(f/e + x^(-1))] + 2*b^2*d*f*(e + f*x)*CosIntegral[2*d*(f/e + x^(-1))]*Sin[2*c - (2*d*f)/e] - 4*a*b*e*f*x*Sin[c + d/x] - 4*a*b*d*e*f*Sin[c - (d*f)/e]*SinIntegral[d*(f/e + x^(-1))] - 4*a*b*d*f^2*x*Sin[c - (d*f)/e]*SinIntegral[d*(f/e + x^(-1))] + 2*b^2*d*e*f*Cos[2*c - (2*d*f)/e]*SinIntegral[2*d*(f/e + x^(-1))] + 2*b^2*d*f^2*x*Cos[2*c - (2*d*f)/e]*SinIntegral[2*d*(f/e + x^(-1))])/(e^2*f*(e + f*x))","A",1
298,1,740,470,3.4887396,"\int \frac{\left(a+b \sin \left(c+\frac{d}{x}\right)\right)^2}{(e+f x)^3} \, dx","Integrate[(a + b*Sin[c + d/x])^2/(e + f*x)^3,x]","-\frac{2 a^2 e^4+4 a b d f (e+f x)^2 \text{Ci}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right) \left(d f \sin \left(c-\frac{d f}{e}\right)+2 e \cos \left(c-\frac{d f}{e}\right)\right)+4 a b d^2 e^2 f^2 \cos \left(c-\frac{d f}{e}\right) \text{Si}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right)+4 a b d^2 f^4 x^2 \cos \left(c-\frac{d f}{e}\right) \text{Si}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right)+8 a b d^2 e f^3 x \cos \left(c-\frac{d f}{e}\right) \text{Si}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right)-8 a b d e^3 f \sin \left(c-\frac{d f}{e}\right) \text{Si}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right)-8 a b e^3 f x \sin \left(c+\frac{d}{x}\right)-16 a b d e^2 f^2 x \sin \left(c-\frac{d f}{e}\right) \text{Si}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right)-4 a b e^2 f^2 x^2 \sin \left(c+\frac{d}{x}\right)+4 a b d e^2 f^2 x \cos \left(c+\frac{d}{x}\right)-8 a b d e f^3 x^2 \sin \left(c-\frac{d f}{e}\right) \text{Si}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right)+4 a b d e f^3 x^2 \cos \left(c+\frac{d}{x}\right)-4 b^2 d f (e+f x)^2 \text{Ci}\left(2 d \left(\frac{f}{e}+\frac{1}{x}\right)\right) \left(d f \cos \left(2 c-\frac{2 d f}{e}\right)-e \sin \left(2 c-\frac{2 d f}{e}\right)\right)+4 b^2 d^2 e^2 f^2 \sin \left(2 c-\frac{2 d f}{e}\right) \text{Si}\left(2 d \left(\frac{f}{e}+\frac{1}{x}\right)\right)+4 b^2 d^2 f^4 x^2 \sin \left(2 c-\frac{2 d f}{e}\right) \text{Si}\left(2 d \left(\frac{f}{e}+\frac{1}{x}\right)\right)+8 b^2 d^2 e f^3 x \sin \left(2 c-\frac{2 d f}{e}\right) \text{Si}\left(2 d \left(\frac{f}{e}+\frac{1}{x}\right)\right)+4 b^2 d e^3 f \cos \left(2 c-\frac{2 d f}{e}\right) \text{Si}\left(2 d \left(\frac{f}{e}+\frac{1}{x}\right)\right)+2 b^2 e^3 f x \cos \left(2 \left(c+\frac{d}{x}\right)\right)+8 b^2 d e^2 f^2 x \cos \left(2 c-\frac{2 d f}{e}\right) \text{Si}\left(2 d \left(\frac{f}{e}+\frac{1}{x}\right)\right)+b^2 e^2 f^2 x^2 \cos \left(2 \left(c+\frac{d}{x}\right)\right)+2 b^2 d e^2 f^2 x \sin \left(2 \left(c+\frac{d}{x}\right)\right)+4 b^2 d e f^3 x^2 \cos \left(2 c-\frac{2 d f}{e}\right) \text{Si}\left(2 d \left(\frac{f}{e}+\frac{1}{x}\right)\right)+2 b^2 d e f^3 x^2 \sin \left(2 \left(c+\frac{d}{x}\right)\right)+b^2 e^4}{4 e^4 f (e+f x)^2}","\frac{a^2}{e^2 \left(\frac{e}{x}+f\right)}-\frac{a^2 f}{2 e^2 \left(\frac{e}{x}+f\right)^2}-\frac{a b d^2 f \sin \left(c-\frac{d f}{e}\right) \text{Ci}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right)}{e^4}-\frac{2 a b d \cos \left(c-\frac{d f}{e}\right) \text{Ci}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right)}{e^3}-\frac{a b d^2 f \cos \left(c-\frac{d f}{e}\right) \text{Si}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right)}{e^4}+\frac{2 a b d \sin \left(c-\frac{d f}{e}\right) \text{Si}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right)}{e^3}-\frac{a b d f \cos \left(c+\frac{d}{x}\right)}{e^3 \left(\frac{e}{x}+f\right)}+\frac{2 a b \sin \left(c+\frac{d}{x}\right)}{e^2 \left(\frac{e}{x}+f\right)}-\frac{a b f \sin \left(c+\frac{d}{x}\right)}{e^2 \left(\frac{e}{x}+f\right)^2}+\frac{b^2 d^2 f \cos \left(2 c-\frac{2 d f}{e}\right) \text{Ci}\left(2 d \left(\frac{f}{e}+\frac{1}{x}\right)\right)}{e^4}-\frac{b^2 d \sin \left(2 c-\frac{2 d f}{e}\right) \text{Ci}\left(2 d \left(\frac{f}{e}+\frac{1}{x}\right)\right)}{e^3}-\frac{b^2 d^2 f \sin \left(2 c-\frac{2 d f}{e}\right) \text{Si}\left(2 d \left(\frac{f}{e}+\frac{1}{x}\right)\right)}{e^4}-\frac{b^2 d \cos \left(2 c-\frac{2 d f}{e}\right) \text{Si}\left(2 d \left(\frac{f}{e}+\frac{1}{x}\right)\right)}{e^3}-\frac{b^2 d f \sin \left(c+\frac{d}{x}\right) \cos \left(c+\frac{d}{x}\right)}{e^3 \left(\frac{e}{x}+f\right)}+\frac{b^2 \sin ^2\left(c+\frac{d}{x}\right)}{e^2 \left(\frac{e}{x}+f\right)}-\frac{b^2 f \sin ^2\left(c+\frac{d}{x}\right)}{2 e^2 \left(\frac{e}{x}+f\right)^2}",1,"-1/4*(2*a^2*e^4 + b^2*e^4 + 4*a*b*d*e^2*f^2*x*Cos[c + d/x] + 4*a*b*d*e*f^3*x^2*Cos[c + d/x] + 2*b^2*e^3*f*x*Cos[2*(c + d/x)] + b^2*e^2*f^2*x^2*Cos[2*(c + d/x)] - 4*b^2*d*f*(e + f*x)^2*CosIntegral[2*d*(f/e + x^(-1))]*(d*f*Cos[2*c - (2*d*f)/e] - e*Sin[2*c - (2*d*f)/e]) + 4*a*b*d*f*(e + f*x)^2*CosIntegral[d*(f/e + x^(-1))]*(2*e*Cos[c - (d*f)/e] + d*f*Sin[c - (d*f)/e]) - 8*a*b*e^3*f*x*Sin[c + d/x] - 4*a*b*e^2*f^2*x^2*Sin[c + d/x] + 2*b^2*d*e^2*f^2*x*Sin[2*(c + d/x)] + 2*b^2*d*e*f^3*x^2*Sin[2*(c + d/x)] + 4*a*b*d^2*e^2*f^2*Cos[c - (d*f)/e]*SinIntegral[d*(f/e + x^(-1))] + 8*a*b*d^2*e*f^3*x*Cos[c - (d*f)/e]*SinIntegral[d*(f/e + x^(-1))] + 4*a*b*d^2*f^4*x^2*Cos[c - (d*f)/e]*SinIntegral[d*(f/e + x^(-1))] - 8*a*b*d*e^3*f*Sin[c - (d*f)/e]*SinIntegral[d*(f/e + x^(-1))] - 16*a*b*d*e^2*f^2*x*Sin[c - (d*f)/e]*SinIntegral[d*(f/e + x^(-1))] - 8*a*b*d*e*f^3*x^2*Sin[c - (d*f)/e]*SinIntegral[d*(f/e + x^(-1))] + 4*b^2*d*e^3*f*Cos[2*c - (2*d*f)/e]*SinIntegral[2*d*(f/e + x^(-1))] + 8*b^2*d*e^2*f^2*x*Cos[2*c - (2*d*f)/e]*SinIntegral[2*d*(f/e + x^(-1))] + 4*b^2*d*e*f^3*x^2*Cos[2*c - (2*d*f)/e]*SinIntegral[2*d*(f/e + x^(-1))] + 4*b^2*d^2*e^2*f^2*Sin[2*c - (2*d*f)/e]*SinIntegral[2*d*(f/e + x^(-1))] + 8*b^2*d^2*e*f^3*x*Sin[2*c - (2*d*f)/e]*SinIntegral[2*d*(f/e + x^(-1))] + 4*b^2*d^2*f^4*x^2*Sin[2*c - (2*d*f)/e]*SinIntegral[2*d*(f/e + x^(-1))])/(e^4*f*(e + f*x)^2)","A",1
299,0,0,25,1.0681039,"\int \frac{(e+f x)^2}{a+b \sin \left(c+\frac{d}{x}\right)} \, dx","Integrate[(e + f*x)^2/(a + b*Sin[c + d/x]),x]","\int \frac{(e+f x)^2}{a+b \sin \left(c+\frac{d}{x}\right)} \, dx","\text{Int}\left(\frac{(e+f x)^2}{a+b \sin \left(c+\frac{d}{x}\right)},x\right)",0,"Integrate[(e + f*x)^2/(a + b*Sin[c + d/x]), x]","A",-1
300,0,0,23,0.5761187,"\int \frac{e+f x}{a+b \sin \left(c+\frac{d}{x}\right)} \, dx","Integrate[(e + f*x)/(a + b*Sin[c + d/x]),x]","\int \frac{e+f x}{a+b \sin \left(c+\frac{d}{x}\right)} \, dx","\text{Int}\left(\frac{e+f x}{a+b \sin \left(c+\frac{d}{x}\right)},x\right)",0,"Integrate[(e + f*x)/(a + b*Sin[c + d/x]), x]","A",-1
301,0,0,17,0.0389182,"\int \frac{1}{a+b \sin \left(c+\frac{d}{x}\right)} \, dx","Integrate[(a + b*Sin[c + d/x])^(-1),x]","\int \frac{1}{a+b \sin \left(c+\frac{d}{x}\right)} \, dx","\text{Int}\left(\frac{1}{a+b \sin \left(c+\frac{d}{x}\right)},x\right)",0,"Integrate[(a + b*Sin[c + d/x])^(-1), x]","A",-1
302,0,0,23,0.0761497,"\int \frac{e+f x}{a+b \sin \left(c+\frac{d}{x}\right)} \, dx","Integrate[(e + f*x)/(a + b*Sin[c + d/x]),x]","\int \frac{e+f x}{a+b \sin \left(c+\frac{d}{x}\right)} \, dx","\text{Int}\left(\frac{e+f x}{a+b \sin \left(c+\frac{d}{x}\right)},x\right)",0,"Integrate[(e + f*x)/(a + b*Sin[c + d/x]), x]","A",-1
303,0,0,25,0.1475947,"\int \frac{(e+f x)^2}{a+b \sin \left(c+\frac{d}{x}\right)} \, dx","Integrate[(e + f*x)^2/(a + b*Sin[c + d/x]),x]","\int \frac{(e+f x)^2}{a+b \sin \left(c+\frac{d}{x}\right)} \, dx","\text{Int}\left(\frac{(e+f x)^2}{a+b \sin \left(c+\frac{d}{x}\right)},x\right)",0,"Integrate[(e + f*x)^2/(a + b*Sin[c + d/x]), x]","A",-1
304,0,0,25,126.3148926,"\int \frac{(e+f x)^2}{\left(a+b \sin \left(c+\frac{d}{x}\right)\right)^2} \, dx","Integrate[(e + f*x)^2/(a + b*Sin[c + d/x])^2,x]","\int \frac{(e+f x)^2}{\left(a+b \sin \left(c+\frac{d}{x}\right)\right)^2} \, dx","\text{Int}\left(\frac{(e+f x)^2}{\left(a+b \sin \left(c+\frac{d}{x}\right)\right)^2},x\right)",0,"Integrate[(e + f*x)^2/(a + b*Sin[c + d/x])^2, x]","A",-1
305,0,0,23,19.4007206,"\int \frac{e+f x}{\left(a+b \sin \left(c+\frac{d}{x}\right)\right)^2} \, dx","Integrate[(e + f*x)/(a + b*Sin[c + d/x])^2,x]","\int \frac{e+f x}{\left(a+b \sin \left(c+\frac{d}{x}\right)\right)^2} \, dx","\text{Int}\left(\frac{e+f x}{\left(a+b \sin \left(c+\frac{d}{x}\right)\right)^2},x\right)",0,"Integrate[(e + f*x)/(a + b*Sin[c + d/x])^2, x]","A",-1
306,0,0,17,3.3744517,"\int \frac{1}{\left(a+b \sin \left(c+\frac{d}{x}\right)\right)^2} \, dx","Integrate[(a + b*Sin[c + d/x])^(-2),x]","\int \frac{1}{\left(a+b \sin \left(c+\frac{d}{x}\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{\left(a+b \sin \left(c+\frac{d}{x}\right)\right)^2},x\right)",0,"Integrate[(a + b*Sin[c + d/x])^(-2), x]","A",-1
307,0,0,23,2.9252873,"\int \frac{e+f x}{\left(a+b \sin \left(c+\frac{d}{x}\right)\right)^2} \, dx","Integrate[(e + f*x)/(a + b*Sin[c + d/x])^2,x]","\int \frac{e+f x}{\left(a+b \sin \left(c+\frac{d}{x}\right)\right)^2} \, dx","\text{Int}\left(\frac{e+f x}{\left(a+b \sin \left(c+\frac{d}{x}\right)\right)^2},x\right)",0,"Integrate[(e + f*x)/(a + b*Sin[c + d/x])^2, x]","A",-1
308,0,0,25,113.1596268,"\int \frac{(e+f x)^2}{\left(a+b \sin \left(c+\frac{d}{x}\right)\right)^2} \, dx","Integrate[(e + f*x)^2/(a + b*Sin[c + d/x])^2,x]","\int \frac{(e+f x)^2}{\left(a+b \sin \left(c+\frac{d}{x}\right)\right)^2} \, dx","\text{Int}\left(\frac{(e+f x)^2}{\left(a+b \sin \left(c+\frac{d}{x}\right)\right)^2},x\right)",0,"Integrate[(e + f*x)^2/(a + b*Sin[c + d/x])^2, x]","A",-1
309,0,0,25,1.4953537,"\int (e+f x)^m \left(a+b \sin \left(c+\frac{d}{x}\right)\right)^p \, dx","Integrate[(e + f*x)^m*(a + b*Sin[c + d/x])^p,x]","\int (e+f x)^m \left(a+b \sin \left(c+\frac{d}{x}\right)\right)^p \, dx","\text{Int}\left((e+f x)^m \left(a+b \sin \left(c+\frac{d}{x}\right)\right)^p,x\right)",0,"Integrate[(e + f*x)^m*(a + b*Sin[c + d/x])^p, x]","A",-1
310,1,94,115,0.1174769,"\int x^m \sqrt[3]{c \sin ^3(a+b x)} \, dx","Integrate[x^m*(c*Sin[a + b*x]^3)^(1/3),x]","-\frac{e^{-i a} x^m \left(b^2 x^2\right)^{-m} \csc (a+b x) \sqrt[3]{c \sin ^3(a+b x)} \left(e^{2 i a} (i b x)^m \Gamma (m+1,-i b x)+(-i b x)^m \Gamma (m+1,i b x)\right)}{2 b}","-\frac{e^{i a} x^m (-i b x)^{-m} \csc (a+b x) \Gamma (m+1,-i b x) \sqrt[3]{c \sin ^3(a+b x)}}{2 b}-\frac{e^{-i a} x^m (i b x)^{-m} \csc (a+b x) \Gamma (m+1,i b x) \sqrt[3]{c \sin ^3(a+b x)}}{2 b}",1,"-1/2*(x^m*Csc[a + b*x]*(E^((2*I)*a)*(I*b*x)^m*Gamma[1 + m, (-I)*b*x] + ((-I)*b*x)^m*Gamma[1 + m, I*b*x])*(c*Sin[a + b*x]^3)^(1/3))/(b*E^(I*a)*(b^2*x^2)^m)","A",1
311,1,47,96,0.2044687,"\int x^3 \sqrt[3]{c \sin ^3(a+b x)} \, dx","Integrate[x^3*(c*Sin[a + b*x]^3)^(1/3),x]","-\frac{\left(b x \left(b^2 x^2-6\right) \cot (a+b x)-3 b^2 x^2+6\right) \sqrt[3]{c \sin ^3(a+b x)}}{b^4}","-\frac{6 \sqrt[3]{c \sin ^3(a+b x)}}{b^4}+\frac{6 x \cot (a+b x) \sqrt[3]{c \sin ^3(a+b x)}}{b^3}+\frac{3 x^2 \sqrt[3]{c \sin ^3(a+b x)}}{b^2}-\frac{x^3 \cot (a+b x) \sqrt[3]{c \sin ^3(a+b x)}}{b}",1,"-(((6 - 3*b^2*x^2 + b*x*(-6 + b^2*x^2)*Cot[a + b*x])*(c*Sin[a + b*x]^3)^(1/3))/b^4)","A",1
312,1,40,74,0.2279475,"\int x^2 \sqrt[3]{c \sin ^3(a+b x)} \, dx","Integrate[x^2*(c*Sin[a + b*x]^3)^(1/3),x]","\frac{\left(\left(2-b^2 x^2\right) \cot (a+b x)+2 b x\right) \sqrt[3]{c \sin ^3(a+b x)}}{b^3}","\frac{2 \cot (a+b x) \sqrt[3]{c \sin ^3(a+b x)}}{b^3}+\frac{2 x \sqrt[3]{c \sin ^3(a+b x)}}{b^2}-\frac{x^2 \cot (a+b x) \sqrt[3]{c \sin ^3(a+b x)}}{b}",1,"((2*b*x + (2 - b^2*x^2)*Cot[a + b*x])*(c*Sin[a + b*x]^3)^(1/3))/b^3","A",1
313,1,30,45,0.1353682,"\int x \sqrt[3]{c \sin ^3(a+b x)} \, dx","Integrate[x*(c*Sin[a + b*x]^3)^(1/3),x]","\frac{(1-b x \cot (a+b x)) \sqrt[3]{c \sin ^3(a+b x)}}{b^2}","\frac{\sqrt[3]{c \sin ^3(a+b x)}}{b^2}-\frac{x \cot (a+b x) \sqrt[3]{c \sin ^3(a+b x)}}{b}",1,"((1 - b*x*Cot[a + b*x])*(c*Sin[a + b*x]^3)^(1/3))/b^2","A",1
314,1,25,25,0.0625763,"\int \sqrt[3]{c \sin ^3(a+b x)} \, dx","Integrate[(c*Sin[a + b*x]^3)^(1/3),x]","-\frac{\cot (a+b x) \sqrt[3]{c \sin ^3(a+b x)}}{b}","-\frac{\cot (a+b x) \sqrt[3]{c \sin ^3(a+b x)}}{b}",1,"-((Cot[a + b*x]*(c*Sin[a + b*x]^3)^(1/3))/b)","A",1
315,1,36,55,0.0533379,"\int \frac{\sqrt[3]{c \sin ^3(a+b x)}}{x} \, dx","Integrate[(c*Sin[a + b*x]^3)^(1/3)/x,x]","\csc (a+b x) \sqrt[3]{c \sin ^3(a+b x)} (\sin (a) \text{Ci}(b x)+\cos (a) \text{Si}(b x))","\sin (a) \text{Ci}(b x) \csc (a+b x) \sqrt[3]{c \sin ^3(a+b x)}+\cos (a) \text{Si}(b x) \csc (a+b x) \sqrt[3]{c \sin ^3(a+b x)}",1,"Csc[a + b*x]*(c*Sin[a + b*x]^3)^(1/3)*(CosIntegral[b*x]*Sin[a] + Cos[a]*SinIntegral[b*x])","A",1
316,1,51,77,0.185866,"\int \frac{\sqrt[3]{c \sin ^3(a+b x)}}{x^2} \, dx","Integrate[(c*Sin[a + b*x]^3)^(1/3)/x^2,x]","\frac{\sqrt[3]{c \sin ^3(a+b x)} (b x \cos (a) \text{Ci}(b x) \csc (a+b x)-b x \sin (a) \text{Si}(b x) \csc (a+b x)-1)}{x}","b \cos (a) \text{Ci}(b x) \csc (a+b x) \sqrt[3]{c \sin ^3(a+b x)}-b \sin (a) \text{Si}(b x) \csc (a+b x) \sqrt[3]{c \sin ^3(a+b x)}-\frac{\sqrt[3]{c \sin ^3(a+b x)}}{x}",1,"((c*Sin[a + b*x]^3)^(1/3)*(-1 + b*x*Cos[a]*CosIntegral[b*x]*Csc[a + b*x] - b*x*Csc[a + b*x]*Sin[a]*SinIntegral[b*x]))/x","A",1
317,1,69,116,0.1447723,"\int \frac{\sqrt[3]{c \sin ^3(a+b x)}}{x^3} \, dx","Integrate[(c*Sin[a + b*x]^3)^(1/3)/x^3,x]","-\frac{\csc (a+b x) \sqrt[3]{c \sin ^3(a+b x)} \left(b^2 x^2 \sin (a) \text{Ci}(b x)+b^2 x^2 \cos (a) \text{Si}(b x)+\sin (a+b x)+b x \cos (a+b x)\right)}{2 x^2}","-\frac{1}{2} b^2 \sin (a) \text{Ci}(b x) \csc (a+b x) \sqrt[3]{c \sin ^3(a+b x)}-\frac{1}{2} b^2 \cos (a) \text{Si}(b x) \csc (a+b x) \sqrt[3]{c \sin ^3(a+b x)}-\frac{\sqrt[3]{c \sin ^3(a+b x)}}{2 x^2}-\frac{b \cot (a+b x) \sqrt[3]{c \sin ^3(a+b x)}}{2 x}",1,"-1/2*(Csc[a + b*x]*(c*Sin[a + b*x]^3)^(1/3)*(b*x*Cos[a + b*x] + b^2*x^2*CosIntegral[b*x]*Sin[a] + Sin[a + b*x] + b^2*x^2*Cos[a]*SinIntegral[b*x]))/x^2","A",1
318,1,138,153,0.3076071,"\int x^m \sqrt[3]{c \sin ^3\left(a+b x^2\right)} \, dx","Integrate[x^m*(c*Sin[a + b*x^2]^3)^(1/3),x]","\frac{1}{4} i x^{m+1} \left(b^2 x^4\right)^{\frac{1}{2} (-m-1)} \csc \left(a+b x^2\right) \sqrt[3]{c \sin ^3\left(a+b x^2\right)} \left((\cos (a)+i \sin (a)) \left(i b x^2\right)^{\frac{m+1}{2}} \Gamma \left(\frac{m+1}{2},-i b x^2\right)-(\cos (a)-i \sin (a)) \left(-i b x^2\right)^{\frac{m+1}{2}} \Gamma \left(\frac{m+1}{2},i b x^2\right)\right)","\frac{1}{4} i e^{i a} x^{m+1} \left(-i b x^2\right)^{\frac{1}{2} (-m-1)} \csc \left(a+b x^2\right) \Gamma \left(\frac{m+1}{2},-i b x^2\right) \sqrt[3]{c \sin ^3\left(a+b x^2\right)}-\frac{1}{4} i e^{-i a} x^{m+1} \left(i b x^2\right)^{\frac{1}{2} (-m-1)} \csc \left(a+b x^2\right) \Gamma \left(\frac{m+1}{2},i b x^2\right) \sqrt[3]{c \sin ^3\left(a+b x^2\right)}",1,"(I/4)*x^(1 + m)*(b^2*x^4)^((-1 - m)/2)*Csc[a + b*x^2]*(-(((-I)*b*x^2)^((1 + m)/2)*Gamma[(1 + m)/2, I*b*x^2]*(Cos[a] - I*Sin[a])) + (I*b*x^2)^((1 + m)/2)*Gamma[(1 + m)/2, (-I)*b*x^2]*(Cos[a] + I*Sin[a]))*(c*Sin[a + b*x^2]^3)^(1/3)","A",1
319,1,38,58,0.0929128,"\int x^3 \sqrt[3]{c \sin ^3\left(a+b x^2\right)} \, dx","Integrate[x^3*(c*Sin[a + b*x^2]^3)^(1/3),x]","-\frac{\left(b x^2 \cot \left(a+b x^2\right)-1\right) \sqrt[3]{c \sin ^3\left(a+b x^2\right)}}{2 b^2}","\frac{\sqrt[3]{c \sin ^3\left(a+b x^2\right)}}{2 b^2}-\frac{x^2 \cot \left(a+b x^2\right) \sqrt[3]{c \sin ^3\left(a+b x^2\right)}}{2 b}",1,"-1/2*((-1 + b*x^2*Cot[a + b*x^2])*(c*Sin[a + b*x^2]^3)^(1/3))/b^2","A",1
320,1,105,155,0.270897,"\int x^2 \sqrt[3]{c \sin ^3\left(a+b x^2\right)} \, dx","Integrate[x^2*(c*Sin[a + b*x^2]^3)^(1/3),x]","-\frac{\csc \left(a+b x^2\right) \sqrt[3]{c \sin ^3\left(a+b x^2\right)} \left(-\sqrt{2 \pi } \cos (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)+\sqrt{2 \pi } \sin (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)+2 \sqrt{b} x \cos \left(a+b x^2\right)\right)}{4 b^{3/2}}","\frac{\sqrt{\frac{\pi }{2}} \cos (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right) \csc \left(a+b x^2\right) \sqrt[3]{c \sin ^3\left(a+b x^2\right)}}{2 b^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} \sin (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right) \csc \left(a+b x^2\right) \sqrt[3]{c \sin ^3\left(a+b x^2\right)}}{2 b^{3/2}}-\frac{x \cot \left(a+b x^2\right) \sqrt[3]{c \sin ^3\left(a+b x^2\right)}}{2 b}",1,"-1/4*(Csc[a + b*x^2]*(2*Sqrt[b]*x*Cos[a + b*x^2] - Sqrt[2*Pi]*Cos[a]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x] + Sqrt[2*Pi]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x]*Sin[a])*(c*Sin[a + b*x^2]^3)^(1/3))/b^(3/2)","A",1
321,1,31,31,0.0551956,"\int x \sqrt[3]{c \sin ^3\left(a+b x^2\right)} \, dx","Integrate[x*(c*Sin[a + b*x^2]^3)^(1/3),x]","-\frac{\cot \left(a+b x^2\right) \sqrt[3]{c \sin ^3\left(a+b x^2\right)}}{2 b}","-\frac{\cot \left(a+b x^2\right) \sqrt[3]{c \sin ^3\left(a+b x^2\right)}}{2 b}",1,"-1/2*(Cot[a + b*x^2]*(c*Sin[a + b*x^2]^3)^(1/3))/b","A",1
322,1,80,117,0.1225352,"\int \sqrt[3]{c \sin ^3\left(a+b x^2\right)} \, dx","Integrate[(c*Sin[a + b*x^2]^3)^(1/3),x]","\frac{\sqrt{\frac{\pi }{2}} \csc \left(a+b x^2\right) \sqrt[3]{c \sin ^3\left(a+b x^2\right)} \left(\sin (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)+\cos (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right)\right)}{\sqrt{b}}","\frac{\sqrt{\frac{\pi }{2}} \sin (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right) \csc \left(a+b x^2\right) \sqrt[3]{c \sin ^3\left(a+b x^2\right)}}{\sqrt{b}}+\frac{\sqrt{\frac{\pi }{2}} \cos (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right) \csc \left(a+b x^2\right) \sqrt[3]{c \sin ^3\left(a+b x^2\right)}}{\sqrt{b}}",1,"(Sqrt[Pi/2]*Csc[a + b*x^2]*(Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x] + FresnelC[Sqrt[b]*Sqrt[2/Pi]*x]*Sin[a])*(c*Sin[a + b*x^2]^3)^(1/3))/Sqrt[b]","A",1
323,1,47,73,0.0591286,"\int \frac{\sqrt[3]{c \sin ^3\left(a+b x^2\right)}}{x} \, dx","Integrate[(c*Sin[a + b*x^2]^3)^(1/3)/x,x]","\frac{1}{2} \csc \left(a+b x^2\right) \sqrt[3]{c \sin ^3\left(a+b x^2\right)} \left(\sin (a) \text{Ci}\left(b x^2\right)+\cos (a) \text{Si}\left(b x^2\right)\right)","\frac{1}{2} \sin (a) \text{Ci}\left(b x^2\right) \csc \left(a+b x^2\right) \sqrt[3]{c \sin ^3\left(a+b x^2\right)}+\frac{1}{2} \cos (a) \text{Si}\left(b x^2\right) \csc \left(a+b x^2\right) \sqrt[3]{c \sin ^3\left(a+b x^2\right)}",1,"(Csc[a + b*x^2]*(c*Sin[a + b*x^2]^3)^(1/3)*(CosIntegral[b*x^2]*Sin[a] + Cos[a]*SinIntegral[b*x^2]))/2","A",1
324,1,105,135,0.28052,"\int \frac{\sqrt[3]{c \sin ^3\left(a+b x^2\right)}}{x^2} \, dx","Integrate[(c*Sin[a + b*x^2]^3)^(1/3)/x^2,x]","\frac{\sqrt[3]{c \sin ^3\left(a+b x^2\right)} \left(\sqrt{2 \pi } \sqrt{b} x \cos (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right) \csc \left(a+b x^2\right)-\sqrt{2 \pi } \sqrt{b} x \sin (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right) \csc \left(a+b x^2\right)-1\right)}{x}","\sqrt{2 \pi } \sqrt{b} \cos (a) C\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right) \csc \left(a+b x^2\right) \sqrt[3]{c \sin ^3\left(a+b x^2\right)}-\sqrt{2 \pi } \sqrt{b} \sin (a) S\left(\sqrt{b} \sqrt{\frac{2}{\pi }} x\right) \csc \left(a+b x^2\right) \sqrt[3]{c \sin ^3\left(a+b x^2\right)}-\frac{\sqrt[3]{c \sin ^3\left(a+b x^2\right)}}{x}",1,"((-1 + Sqrt[b]*Sqrt[2*Pi]*x*Cos[a]*Csc[a + b*x^2]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x] - Sqrt[b]*Sqrt[2*Pi]*x*Csc[a + b*x^2]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x]*Sin[a])*(c*Sin[a + b*x^2]^3)^(1/3))/x","A",1
325,1,67,98,0.1258088,"\int \frac{\sqrt[3]{c \sin ^3\left(a+b x^2\right)}}{x^3} \, dx","Integrate[(c*Sin[a + b*x^2]^3)^(1/3)/x^3,x]","-\frac{\csc \left(a+b x^2\right) \sqrt[3]{c \sin ^3\left(a+b x^2\right)} \left(-b x^2 \cos (a) \text{Ci}\left(b x^2\right)+b x^2 \sin (a) \text{Si}\left(b x^2\right)+\sin \left(a+b x^2\right)\right)}{2 x^2}","\frac{1}{2} b \cos (a) \text{Ci}\left(b x^2\right) \csc \left(a+b x^2\right) \sqrt[3]{c \sin ^3\left(a+b x^2\right)}-\frac{1}{2} b \sin (a) \text{Si}\left(b x^2\right) \csc \left(a+b x^2\right) \sqrt[3]{c \sin ^3\left(a+b x^2\right)}-\frac{\sqrt[3]{c \sin ^3\left(a+b x^2\right)}}{2 x^2}",1,"-1/2*(Csc[a + b*x^2]*(c*Sin[a + b*x^2]^3)^(1/3)*(-(b*x^2*Cos[a]*CosIntegral[b*x^2]) + Sin[a + b*x^2] + b*x^2*Sin[a]*SinIntegral[b*x^2]))/x^2","A",1
326,1,142,157,0.3512681,"\int x^m \sqrt[3]{c \sin ^3\left(a+b x^n\right)} \, dx","Integrate[x^m*(c*Sin[a + b*x^n]^3)^(1/3),x]","\frac{i x^{m+1} \left(b^2 x^{2 n}\right)^{-\frac{m+1}{n}} \csc \left(a+b x^n\right) \sqrt[3]{c \sin ^3\left(a+b x^n\right)} \left((\cos (a)+i \sin (a)) \left(i b x^n\right)^{\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-i b x^n\right)-(\cos (a)-i \sin (a)) \left(-i b x^n\right)^{\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},i b x^n\right)\right)}{2 n}","\frac{i e^{i a} x^{m+1} \left(-i b x^n\right)^{-\frac{m+1}{n}} \csc \left(a+b x^n\right) \Gamma \left(\frac{m+1}{n},-i b x^n\right) \sqrt[3]{c \sin ^3\left(a+b x^n\right)}}{2 n}-\frac{i e^{-i a} x^{m+1} \left(i b x^n\right)^{-\frac{m+1}{n}} \csc \left(a+b x^n\right) \Gamma \left(\frac{m+1}{n},i b x^n\right) \sqrt[3]{c \sin ^3\left(a+b x^n\right)}}{2 n}",1,"((I/2)*x^(1 + m)*Csc[a + b*x^n]*(-(((-I)*b*x^n)^((1 + m)/n)*Gamma[(1 + m)/n, I*b*x^n]*(Cos[a] - I*Sin[a])) + (I*b*x^n)^((1 + m)/n)*Gamma[(1 + m)/n, (-I)*b*x^n]*(Cos[a] + I*Sin[a]))*(c*Sin[a + b*x^n]^3)^(1/3))/(n*(b^2*x^(2*n))^((1 + m)/n))","A",1
327,1,129,143,0.1994965,"\int x^3 \sqrt[3]{c \sin ^3\left(a+b x^n\right)} \, dx","Integrate[x^3*(c*Sin[a + b*x^n]^3)^(1/3),x]","\frac{i x^4 \left(b^2 x^{2 n}\right)^{-4/n} \csc \left(a+b x^n\right) \sqrt[3]{c \sin ^3\left(a+b x^n\right)} \left((\cos (a)+i \sin (a)) \left(i b x^n\right)^{4/n} \Gamma \left(\frac{4}{n},-i b x^n\right)-(\cos (a)-i \sin (a)) \left(-i b x^n\right)^{4/n} \Gamma \left(\frac{4}{n},i b x^n\right)\right)}{2 n}","\frac{i e^{i a} x^4 \left(-i b x^n\right)^{-4/n} \Gamma \left(\frac{4}{n},-i b x^n\right) \csc \left(a+b x^n\right) \sqrt[3]{c \sin ^3\left(a+b x^n\right)}}{2 n}-\frac{i e^{-i a} x^4 \left(i b x^n\right)^{-4/n} \Gamma \left(\frac{4}{n},i b x^n\right) \csc \left(a+b x^n\right) \sqrt[3]{c \sin ^3\left(a+b x^n\right)}}{2 n}",1,"((I/2)*x^4*Csc[a + b*x^n]*(-(((-I)*b*x^n)^(4/n)*Gamma[4/n, I*b*x^n]*(Cos[a] - I*Sin[a])) + (I*b*x^n)^(4/n)*Gamma[4/n, (-I)*b*x^n]*(Cos[a] + I*Sin[a]))*(c*Sin[a + b*x^n]^3)^(1/3))/(n*(b^2*x^(2*n))^(4/n))","A",1
328,1,129,143,0.1876592,"\int x^2 \sqrt[3]{c \sin ^3\left(a+b x^n\right)} \, dx","Integrate[x^2*(c*Sin[a + b*x^n]^3)^(1/3),x]","\frac{i x^3 \left(b^2 x^{2 n}\right)^{-3/n} \csc \left(a+b x^n\right) \sqrt[3]{c \sin ^3\left(a+b x^n\right)} \left((\cos (a)+i \sin (a)) \left(i b x^n\right)^{3/n} \Gamma \left(\frac{3}{n},-i b x^n\right)-(\cos (a)-i \sin (a)) \left(-i b x^n\right)^{3/n} \Gamma \left(\frac{3}{n},i b x^n\right)\right)}{2 n}","\frac{i e^{i a} x^3 \left(-i b x^n\right)^{-3/n} \Gamma \left(\frac{3}{n},-i b x^n\right) \csc \left(a+b x^n\right) \sqrt[3]{c \sin ^3\left(a+b x^n\right)}}{2 n}-\frac{i e^{-i a} x^3 \left(i b x^n\right)^{-3/n} \Gamma \left(\frac{3}{n},i b x^n\right) \csc \left(a+b x^n\right) \sqrt[3]{c \sin ^3\left(a+b x^n\right)}}{2 n}",1,"((I/2)*x^3*Csc[a + b*x^n]*(-(((-I)*b*x^n)^(3/n)*Gamma[3/n, I*b*x^n]*(Cos[a] - I*Sin[a])) + (I*b*x^n)^(3/n)*Gamma[3/n, (-I)*b*x^n]*(Cos[a] + I*Sin[a]))*(c*Sin[a + b*x^n]^3)^(1/3))/(n*(b^2*x^(2*n))^(3/n))","A",1
329,1,129,143,0.1810232,"\int x \sqrt[3]{c \sin ^3\left(a+b x^n\right)} \, dx","Integrate[x*(c*Sin[a + b*x^n]^3)^(1/3),x]","\frac{i x^2 \left(b^2 x^{2 n}\right)^{-2/n} \csc \left(a+b x^n\right) \sqrt[3]{c \sin ^3\left(a+b x^n\right)} \left((\cos (a)+i \sin (a)) \left(i b x^n\right)^{2/n} \Gamma \left(\frac{2}{n},-i b x^n\right)-(\cos (a)-i \sin (a)) \left(-i b x^n\right)^{2/n} \Gamma \left(\frac{2}{n},i b x^n\right)\right)}{2 n}","\frac{i e^{i a} x^2 \left(-i b x^n\right)^{-2/n} \Gamma \left(\frac{2}{n},-i b x^n\right) \csc \left(a+b x^n\right) \sqrt[3]{c \sin ^3\left(a+b x^n\right)}}{2 n}-\frac{i e^{-i a} x^2 \left(i b x^n\right)^{-2/n} \Gamma \left(\frac{2}{n},i b x^n\right) \csc \left(a+b x^n\right) \sqrt[3]{c \sin ^3\left(a+b x^n\right)}}{2 n}",1,"((I/2)*x^2*Csc[a + b*x^n]*(-(((-I)*b*x^n)^(2/n)*Gamma[2/n, I*b*x^n]*(Cos[a] - I*Sin[a])) + (I*b*x^n)^(2/n)*Gamma[2/n, (-I)*b*x^n]*(Cos[a] + I*Sin[a]))*(c*Sin[a + b*x^n]^3)^(1/3))/(n*(b^2*x^(2*n))^(2/n))","A",1
330,1,119,135,0.1384828,"\int \sqrt[3]{c \sin ^3\left(a+b x^n\right)} \, dx","Integrate[(c*Sin[a + b*x^n]^3)^(1/3),x]","\frac{i x \left(b^2 x^{2 n}\right)^{-1/n} \csc \left(a+b x^n\right) \sqrt[3]{c \sin ^3\left(a+b x^n\right)} \left((\cos (a)+i \sin (a)) \left(i b x^n\right)^{\frac{1}{n}} \Gamma \left(\frac{1}{n},-i b x^n\right)-(\cos (a)-i \sin (a)) \left(-i b x^n\right)^{\frac{1}{n}} \Gamma \left(\frac{1}{n},i b x^n\right)\right)}{2 n}","\frac{i e^{i a} x \left(-i b x^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-i b x^n\right) \csc \left(a+b x^n\right) \sqrt[3]{c \sin ^3\left(a+b x^n\right)}}{2 n}-\frac{i e^{-i a} x \left(i b x^n\right)^{-1/n} \Gamma \left(\frac{1}{n},i b x^n\right) \csc \left(a+b x^n\right) \sqrt[3]{c \sin ^3\left(a+b x^n\right)}}{2 n}",1,"((I/2)*x*Csc[a + b*x^n]*(-(((-I)*b*x^n)^n^(-1)*Gamma[n^(-1), I*b*x^n]*(Cos[a] - I*Sin[a])) + (I*b*x^n)^n^(-1)*Gamma[n^(-1), (-I)*b*x^n]*(Cos[a] + I*Sin[a]))*(c*Sin[a + b*x^n]^3)^(1/3))/(n*(b^2*x^(2*n))^n^(-1))","A",1
331,1,47,73,0.0779407,"\int \frac{\sqrt[3]{c \sin ^3\left(a+b x^n\right)}}{x} \, dx","Integrate[(c*Sin[a + b*x^n]^3)^(1/3)/x,x]","\frac{\csc \left(a+b x^n\right) \sqrt[3]{c \sin ^3\left(a+b x^n\right)} \left(\sin (a) \text{Ci}\left(b x^n\right)+\cos (a) \text{Si}\left(b x^n\right)\right)}{n}","\frac{\sin (a) \text{Ci}\left(b x^n\right) \csc \left(a+b x^n\right) \sqrt[3]{c \sin ^3\left(a+b x^n\right)}}{n}+\frac{\cos (a) \text{Si}\left(b x^n\right) \csc \left(a+b x^n\right) \sqrt[3]{c \sin ^3\left(a+b x^n\right)}}{n}",1,"(Csc[a + b*x^n]*(c*Sin[a + b*x^n]^3)^(1/3)*(CosIntegral[b*x^n]*Sin[a] + Cos[a]*SinIntegral[b*x^n]))/n","A",1
332,1,110,139,0.1603534,"\int \frac{\sqrt[3]{c \sin ^3\left(a+b x^n\right)}}{x^2} \, dx","Integrate[(c*Sin[a + b*x^n]^3)^(1/3)/x^2,x]","\frac{i \csc \left(a+b x^n\right) \sqrt[3]{c \sin ^3\left(a+b x^n\right)} \left((\cos (a)+i \sin (a)) \left(-i b x^n\right)^{\frac{1}{n}} \Gamma \left(-\frac{1}{n},-i b x^n\right)-(\cos (a)-i \sin (a)) \left(i b x^n\right)^{\frac{1}{n}} \Gamma \left(-\frac{1}{n},i b x^n\right)\right)}{2 n x}","\frac{i e^{i a} \left(-i b x^n\right)^{\frac{1}{n}} \Gamma \left(-\frac{1}{n},-i b x^n\right) \csc \left(a+b x^n\right) \sqrt[3]{c \sin ^3\left(a+b x^n\right)}}{2 n x}-\frac{i e^{-i a} \left(i b x^n\right)^{\frac{1}{n}} \Gamma \left(-\frac{1}{n},i b x^n\right) \csc \left(a+b x^n\right) \sqrt[3]{c \sin ^3\left(a+b x^n\right)}}{2 n x}",1,"((I/2)*Csc[a + b*x^n]*(-((I*b*x^n)^n^(-1)*Gamma[-n^(-1), I*b*x^n]*(Cos[a] - I*Sin[a])) + ((-I)*b*x^n)^n^(-1)*Gamma[-n^(-1), (-I)*b*x^n]*(Cos[a] + I*Sin[a]))*(c*Sin[a + b*x^n]^3)^(1/3))/(n*x)","A",1
333,1,114,143,0.1719844,"\int \frac{\sqrt[3]{c \sin ^3\left(a+b x^n\right)}}{x^3} \, dx","Integrate[(c*Sin[a + b*x^n]^3)^(1/3)/x^3,x]","\frac{i \csc \left(a+b x^n\right) \sqrt[3]{c \sin ^3\left(a+b x^n\right)} \left((\cos (a)+i \sin (a)) \left(-i b x^n\right)^{2/n} \Gamma \left(-\frac{2}{n},-i b x^n\right)-(\cos (a)-i \sin (a)) \left(i b x^n\right)^{2/n} \Gamma \left(-\frac{2}{n},i b x^n\right)\right)}{2 n x^2}","\frac{i e^{i a} \left(-i b x^n\right)^{2/n} \Gamma \left(-\frac{2}{n},-i b x^n\right) \csc \left(a+b x^n\right) \sqrt[3]{c \sin ^3\left(a+b x^n\right)}}{2 n x^2}-\frac{i e^{-i a} \left(i b x^n\right)^{2/n} \Gamma \left(-\frac{2}{n},i b x^n\right) \csc \left(a+b x^n\right) \sqrt[3]{c \sin ^3\left(a+b x^n\right)}}{2 n x^2}",1,"((I/2)*Csc[a + b*x^n]*(-((I*b*x^n)^(2/n)*Gamma[-2/n, I*b*x^n]*(Cos[a] - I*Sin[a])) + ((-I)*b*x^n)^(2/n)*Gamma[-2/n, (-I)*b*x^n]*(Cos[a] + I*Sin[a]))*(c*Sin[a + b*x^n]^3)^(1/3))/(n*x^2)","A",1
334,1,142,169,0.5267812,"\int x^m \left(c \sin ^3(a+b x)\right)^{2/3} \, dx","Integrate[x^m*(c*Sin[a + b*x]^3)^(2/3),x]","\frac{2^{-m-3} x^m \left(b^2 x^2\right)^{-m} \csc ^2(a+b x) \left(c \sin ^3(a+b x)\right)^{2/3} \left(-i (m+1) (\cos (a)-i \sin (a))^2 (-i b x)^m \Gamma (m+1,2 i b x)+i (m+1) (\cos (a)+i \sin (a))^2 (i b x)^m \Gamma (m+1,-2 i b x)+b 2^{m+2} x \left(b^2 x^2\right)^m\right)}{b (m+1)}","\frac{x^{m+1} \csc ^2(a+b x) \left(c \sin ^3(a+b x)\right)^{2/3}}{2 (m+1)}+\frac{i e^{2 i a} 2^{-m-3} x^m (-i b x)^{-m} \csc ^2(a+b x) \Gamma (m+1,-2 i b x) \left(c \sin ^3(a+b x)\right)^{2/3}}{b}-\frac{i e^{-2 i a} 2^{-m-3} x^m (i b x)^{-m} \csc ^2(a+b x) \Gamma (m+1,2 i b x) \left(c \sin ^3(a+b x)\right)^{2/3}}{b}",1,"(2^(-3 - m)*x^m*Csc[a + b*x]^2*(2^(2 + m)*b*x*(b^2*x^2)^m - I*(1 + m)*((-I)*b*x)^m*Gamma[1 + m, (2*I)*b*x]*(Cos[a] - I*Sin[a])^2 + I*(1 + m)*(I*b*x)^m*Gamma[1 + m, (-2*I)*b*x]*(Cos[a] + I*Sin[a])^2)*(c*Sin[a + b*x]^3)^(2/3))/(b*(1 + m)*(b^2*x^2)^m)","A",1
335,1,79,165,0.2954352,"\int x^3 \left(c \sin ^3(a+b x)\right)^{2/3} \, dx","Integrate[x^3*(c*Sin[a + b*x]^3)^(2/3),x]","\frac{\csc ^2(a+b x) \left(c \sin ^3(a+b x)\right)^{2/3} \left(\left(6 b x-4 b^3 x^3\right) \sin (2 (a+b x))+\left(3-6 b^2 x^2\right) \cos (2 (a+b x))+2 b^4 x^4\right)}{16 b^4}","-\frac{3 \left(c \sin ^3(a+b x)\right)^{2/3}}{8 b^4}+\frac{3 x \cot (a+b x) \left(c \sin ^3(a+b x)\right)^{2/3}}{4 b^3}+\frac{3 x^2 \left(c \sin ^3(a+b x)\right)^{2/3}}{4 b^2}-\frac{3 x^2 \csc ^2(a+b x) \left(c \sin ^3(a+b x)\right)^{2/3}}{8 b^2}+\frac{1}{8} x^4 \csc ^2(a+b x) \left(c \sin ^3(a+b x)\right)^{2/3}-\frac{x^3 \cot (a+b x) \left(c \sin ^3(a+b x)\right)^{2/3}}{2 b}",1,"(Csc[a + b*x]^2*(c*Sin[a + b*x]^3)^(2/3)*(2*b^4*x^4 + (3 - 6*b^2*x^2)*Cos[2*(a + b*x)] + (6*b*x - 4*b^3*x^3)*Sin[2*(a + b*x)]))/(16*b^4)","A",1
336,1,69,139,0.2806946,"\int x^2 \left(c \sin ^3(a+b x)\right)^{2/3} \, dx","Integrate[x^2*(c*Sin[a + b*x]^3)^(2/3),x]","\frac{\csc ^2(a+b x) \left(c \sin ^3(a+b x)\right)^{2/3} \left(\left(3-6 b^2 x^2\right) \sin (2 (a+b x))-6 b x \cos (2 (a+b x))+4 b^3 x^3\right)}{24 b^3}","\frac{\cot (a+b x) \left(c \sin ^3(a+b x)\right)^{2/3}}{4 b^3}+\frac{x \left(c \sin ^3(a+b x)\right)^{2/3}}{2 b^2}-\frac{x \csc ^2(a+b x) \left(c \sin ^3(a+b x)\right)^{2/3}}{4 b^2}+\frac{1}{6} x^3 \csc ^2(a+b x) \left(c \sin ^3(a+b x)\right)^{2/3}-\frac{x^2 \cot (a+b x) \left(c \sin ^3(a+b x)\right)^{2/3}}{2 b}",1,"(Csc[a + b*x]^2*(c*Sin[a + b*x]^3)^(2/3)*(4*b^3*x^3 - 6*b*x*Cos[2*(a + b*x)] + (3 - 6*b^2*x^2)*Sin[2*(a + b*x)]))/(24*b^3)","A",1
337,1,55,79,0.1759714,"\int x \left(c \sin ^3(a+b x)\right)^{2/3} \, dx","Integrate[x*(c*Sin[a + b*x]^3)^(2/3),x]","-\frac{\csc ^2(a+b x) \left(c \sin ^3(a+b x)\right)^{2/3} (2 b x (\sin (2 (a+b x))-b x)+\cos (2 (a+b x)))}{8 b^2}","\frac{\left(c \sin ^3(a+b x)\right)^{2/3}}{4 b^2}+\frac{1}{4} x^2 \csc ^2(a+b x) \left(c \sin ^3(a+b x)\right)^{2/3}-\frac{x \cot (a+b x) \left(c \sin ^3(a+b x)\right)^{2/3}}{2 b}",1,"-1/8*(Csc[a + b*x]^2*(c*Sin[a + b*x]^3)^(2/3)*(Cos[2*(a + b*x)] + 2*b*x*(-(b*x) + Sin[2*(a + b*x)])))/b^2","A",1
338,1,47,55,0.0954081,"\int \left(c \sin ^3(a+b x)\right)^{2/3} \, dx","Integrate[(c*Sin[a + b*x]^3)^(2/3),x]","\frac{(2 (a+b x)-\sin (2 (a+b x))) \csc ^2(a+b x) \left(c \sin ^3(a+b x)\right)^{2/3}}{4 b}","\frac{1}{2} x \csc ^2(a+b x) \left(c \sin ^3(a+b x)\right)^{2/3}-\frac{\cot (a+b x) \left(c \sin ^3(a+b x)\right)^{2/3}}{2 b}",1,"(Csc[a + b*x]^2*(c*Sin[a + b*x]^3)^(2/3)*(2*(a + b*x) - Sin[2*(a + b*x)]))/(4*b)","A",1
339,1,50,99,0.08358,"\int \frac{\left(c \sin ^3(a+b x)\right)^{2/3}}{x} \, dx","Integrate[(c*Sin[a + b*x]^3)^(2/3)/x,x]","\frac{1}{2} \csc ^2(a+b x) \left(c \sin ^3(a+b x)\right)^{2/3} (-\cos (2 a) \text{Ci}(2 b x)+\sin (2 a) \text{Si}(2 b x)+\log (x))","-\frac{1}{2} \cos (2 a) \text{Ci}(2 b x) \csc ^2(a+b x) \left(c \sin ^3(a+b x)\right)^{2/3}+\frac{1}{2} \sin (2 a) \text{Si}(2 b x) \csc ^2(a+b x) \left(c \sin ^3(a+b x)\right)^{2/3}+\frac{1}{2} \log (x) \csc ^2(a+b x) \left(c \sin ^3(a+b x)\right)^{2/3}",1,"(Csc[a + b*x]^2*(c*Sin[a + b*x]^3)^(2/3)*(-(Cos[2*a]*CosIntegral[2*b*x]) + Log[x] + Sin[2*a]*SinIntegral[2*b*x]))/2","A",1
340,1,65,86,0.1496743,"\int \frac{\left(c \sin ^3(a+b x)\right)^{2/3}}{x^2} \, dx","Integrate[(c*Sin[a + b*x]^3)^(2/3)/x^2,x]","\frac{\csc ^2(a+b x) \left(c \sin ^3(a+b x)\right)^{2/3} (2 b x \sin (2 a) \text{Ci}(2 b x)+2 b x \cos (2 a) \text{Si}(2 b x)+\cos (2 (a+b x))-1)}{2 x}","b \sin (2 a) \text{Ci}(2 b x) \csc ^2(a+b x) \left(c \sin ^3(a+b x)\right)^{2/3}+b \cos (2 a) \text{Si}(2 b x) \csc ^2(a+b x) \left(c \sin ^3(a+b x)\right)^{2/3}-\frac{\left(c \sin ^3(a+b x)\right)^{2/3}}{x}",1,"(Csc[a + b*x]^2*(c*Sin[a + b*x]^3)^(2/3)*(-1 + Cos[2*(a + b*x)] + 2*b*x*CosIntegral[2*b*x]*Sin[2*a] + 2*b*x*Cos[2*a]*SinIntegral[2*b*x]))/(2*x)","A",1
341,1,85,119,0.2068747,"\int \frac{\left(c \sin ^3(a+b x)\right)^{2/3}}{x^3} \, dx","Integrate[(c*Sin[a + b*x]^3)^(2/3)/x^3,x]","\frac{\csc ^2(a+b x) \left(c \sin ^3(a+b x)\right)^{2/3} \left(4 b^2 x^2 \cos (2 a) \text{Ci}(2 b x)-4 b^2 x^2 \sin (2 a) \text{Si}(2 b x)-2 b x \sin (2 (a+b x))+\cos (2 (a+b x))-1\right)}{4 x^2}","b^2 \cos (2 a) \text{Ci}(2 b x) \csc ^2(a+b x) \left(c \sin ^3(a+b x)\right)^{2/3}-b^2 \sin (2 a) \text{Si}(2 b x) \csc ^2(a+b x) \left(c \sin ^3(a+b x)\right)^{2/3}-\frac{\left(c \sin ^3(a+b x)\right)^{2/3}}{2 x^2}-\frac{b \cot (a+b x) \left(c \sin ^3(a+b x)\right)^{2/3}}{x}",1,"(Csc[a + b*x]^2*(c*Sin[a + b*x]^3)^(2/3)*(-1 + Cos[2*(a + b*x)] + 4*b^2*x^2*Cos[2*a]*CosIntegral[2*b*x] - 2*b*x*Sin[2*(a + b*x)] - 4*b^2*x^2*Sin[2*a]*SinIntegral[2*b*x]))/(4*x^2)","A",1
342,1,189,209,0.8932338,"\int x^m \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3} \, dx","Integrate[x^m*(c*Sin[a + b*x^2]^3)^(2/3),x]","\frac{2^{\frac{1}{2} (-m-7)} x^{m+1} \left(b^2 x^4\right)^{\frac{1}{2} (-m-1)} \csc ^2\left(a+b x^2\right) \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3} \left((m+1) (\cos (2 a)-i \sin (2 a)) \left(-i b x^2\right)^{\frac{m+1}{2}} \Gamma \left(\frac{m+1}{2},2 i b x^2\right)+(m+1) (\cos (2 a)+i \sin (2 a)) \left(i b x^2\right)^{\frac{m+1}{2}} \Gamma \left(\frac{m+1}{2},-2 i b x^2\right)+2^{\frac{m+5}{2}} \left(b^2 x^4\right)^{\frac{m+1}{2}}\right)}{m+1}","\frac{x^{m+1} \csc ^2\left(a+b x^2\right) \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3}}{2 (m+1)}+e^{2 i a} 2^{-\frac{m}{2}-\frac{7}{2}} x^{m+1} \left(-i b x^2\right)^{\frac{1}{2} (-m-1)} \csc ^2\left(a+b x^2\right) \Gamma \left(\frac{m+1}{2},-2 i b x^2\right) \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3}+e^{-2 i a} 2^{-\frac{m}{2}-\frac{7}{2}} x^{m+1} \left(i b x^2\right)^{\frac{1}{2} (-m-1)} \csc ^2\left(a+b x^2\right) \Gamma \left(\frac{m+1}{2},2 i b x^2\right) \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3}",1,"(2^((-7 - m)/2)*x^(1 + m)*(b^2*x^4)^((-1 - m)/2)*Csc[a + b*x^2]^2*(2^((5 + m)/2)*(b^2*x^4)^((1 + m)/2) + (1 + m)*((-I)*b*x^2)^((1 + m)/2)*Gamma[(1 + m)/2, (2*I)*b*x^2]*(Cos[2*a] - I*Sin[2*a]) + (1 + m)*(I*b*x^2)^((1 + m)/2)*Gamma[(1 + m)/2, (-2*I)*b*x^2]*(Cos[2*a] + I*Sin[2*a]))*(c*Sin[a + b*x^2]^3)^(2/3))/(1 + m)","A",1
343,1,67,91,0.2333469,"\int x^3 \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3} \, dx","Integrate[x^3*(c*Sin[a + b*x^2]^3)^(2/3),x]","-\frac{\csc ^2\left(a+b x^2\right) \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3} \left(2 b x^2 \left(\sin \left(2 \left(a+b x^2\right)\right)-b x^2\right)+\cos \left(2 \left(a+b x^2\right)\right)\right)}{16 b^2}","\frac{\left(c \sin ^3\left(a+b x^2\right)\right)^{2/3}}{8 b^2}-\frac{x^2 \cot \left(a+b x^2\right) \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3}}{4 b}+\frac{1}{8} x^4 \csc ^2\left(a+b x^2\right) \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3}",1,"-1/16*(Csc[a + b*x^2]^2*(c*Sin[a + b*x^2]^3)^(2/3)*(Cos[2*(a + b*x^2)] + 2*b*x^2*(-(b*x^2) + Sin[2*(a + b*x^2)])))/b^2","A",1
344,1,113,195,0.2868553,"\int x^2 \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3} \, dx","Integrate[x^2*(c*Sin[a + b*x^2]^3)^(2/3),x]","\frac{\csc ^2\left(a+b x^2\right) \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3} \left(3 \sqrt{\pi } \sin (2 a) C\left(\frac{2 \sqrt{b} x}{\sqrt{\pi }}\right)+3 \sqrt{\pi } \cos (2 a) S\left(\frac{2 \sqrt{b} x}{\sqrt{\pi }}\right)+2 \sqrt{b} x \left(4 b x^2-3 \sin \left(2 \left(a+b x^2\right)\right)\right)\right)}{48 b^{3/2}}","\frac{\sqrt{\pi } \sin (2 a) C\left(\frac{2 \sqrt{b} x}{\sqrt{\pi }}\right) \csc ^2\left(a+b x^2\right) \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3}}{16 b^{3/2}}+\frac{\sqrt{\pi } \cos (2 a) S\left(\frac{2 \sqrt{b} x}{\sqrt{\pi }}\right) \csc ^2\left(a+b x^2\right) \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3}}{16 b^{3/2}}-\frac{x \sin \left(2 a+2 b x^2\right) \csc ^2\left(a+b x^2\right) \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3}}{8 b}+\frac{1}{6} x^3 \csc ^2\left(a+b x^2\right) \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3}",1,"(Csc[a + b*x^2]^2*(c*Sin[a + b*x^2]^3)^(2/3)*(3*Sqrt[Pi]*Cos[2*a]*FresnelS[(2*Sqrt[b]*x)/Sqrt[Pi]] + 3*Sqrt[Pi]*FresnelC[(2*Sqrt[b]*x)/Sqrt[Pi]]*Sin[2*a] + 2*Sqrt[b]*x*(4*b*x^2 - 3*Sin[2*(a + b*x^2)])))/(48*b^(3/2))","A",1
345,1,55,65,0.1141936,"\int x \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3} \, dx","Integrate[x*(c*Sin[a + b*x^2]^3)^(2/3),x]","\frac{\left(2 \left(a+b x^2\right)-\sin \left(2 \left(a+b x^2\right)\right)\right) \csc ^2\left(a+b x^2\right) \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3}}{8 b}","\frac{1}{4} x^2 \csc ^2\left(a+b x^2\right) \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3}-\frac{\cot \left(a+b x^2\right) \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3}}{4 b}",1,"(Csc[a + b*x^2]^2*(c*Sin[a + b*x^2]^3)^(2/3)*(2*(a + b*x^2) - Sin[2*(a + b*x^2)]))/(8*b)","A",1
346,1,93,148,0.1017154,"\int \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3} \, dx","Integrate[(c*Sin[a + b*x^2]^3)^(2/3),x]","\frac{\csc ^2\left(a+b x^2\right) \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3} \left(-\sqrt{\pi } \cos (2 a) C\left(\frac{2 \sqrt{b} x}{\sqrt{\pi }}\right)+\sqrt{\pi } \sin (2 a) S\left(\frac{2 \sqrt{b} x}{\sqrt{\pi }}\right)+2 \sqrt{b} x\right)}{4 \sqrt{b}}","-\frac{\sqrt{\pi } \cos (2 a) C\left(\frac{2 \sqrt{b} x}{\sqrt{\pi }}\right) \csc ^2\left(a+b x^2\right) \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3}}{4 \sqrt{b}}+\frac{\sqrt{\pi } \sin (2 a) S\left(\frac{2 \sqrt{b} x}{\sqrt{\pi }}\right) \csc ^2\left(a+b x^2\right) \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3}}{4 \sqrt{b}}+\frac{1}{2} x \csc ^2\left(a+b x^2\right) \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3}",1,"(Csc[a + b*x^2]^2*(2*Sqrt[b]*x - Sqrt[Pi]*Cos[2*a]*FresnelC[(2*Sqrt[b]*x)/Sqrt[Pi]] + Sqrt[Pi]*FresnelS[(2*Sqrt[b]*x)/Sqrt[Pi]]*Sin[2*a])*(c*Sin[a + b*x^2]^3)^(2/3))/(4*Sqrt[b])","A",1
347,1,60,115,0.0967347,"\int \frac{\left(c \sin ^3\left(a+b x^2\right)\right)^{2/3}}{x} \, dx","Integrate[(c*Sin[a + b*x^2]^3)^(2/3)/x,x]","\frac{1}{4} \csc ^2\left(a+b x^2\right) \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3} \left(-\cos (2 a) \text{Ci}\left(2 b x^2\right)+\sin (2 a) \text{Si}\left(2 b x^2\right)+2 \log (x)\right)","-\frac{1}{4} \cos (2 a) \text{Ci}\left(2 b x^2\right) \csc ^2\left(a+b x^2\right) \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3}+\frac{1}{4} \sin (2 a) \text{Si}\left(2 b x^2\right) \csc ^2\left(a+b x^2\right) \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3}+\frac{1}{2} \log (x) \csc ^2\left(a+b x^2\right) \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3}",1,"(Csc[a + b*x^2]^2*(c*Sin[a + b*x^2]^3)^(2/3)*(-(Cos[2*a]*CosIntegral[2*b*x^2]) + 2*Log[x] + Sin[2*a]*SinIntegral[2*b*x^2]))/4","A",1
348,1,107,132,0.2045524,"\int \frac{\left(c \sin ^3\left(a+b x^2\right)\right)^{2/3}}{x^2} \, dx","Integrate[(c*Sin[a + b*x^2]^3)^(2/3)/x^2,x]","\frac{\csc ^2\left(a+b x^2\right) \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3} \left(2 \sqrt{\pi } \sqrt{b} x \sin (2 a) C\left(\frac{2 \sqrt{b} x}{\sqrt{\pi }}\right)+2 \sqrt{\pi } \sqrt{b} x \cos (2 a) S\left(\frac{2 \sqrt{b} x}{\sqrt{\pi }}\right)+\cos \left(2 \left(a+b x^2\right)\right)-1\right)}{2 x}","\sqrt{\pi } \sqrt{b} \sin (2 a) C\left(\frac{2 \sqrt{b} x}{\sqrt{\pi }}\right) \csc ^2\left(a+b x^2\right) \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3}+\sqrt{\pi } \sqrt{b} \cos (2 a) S\left(\frac{2 \sqrt{b} x}{\sqrt{\pi }}\right) \csc ^2\left(a+b x^2\right) \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3}-\frac{\left(c \sin ^3\left(a+b x^2\right)\right)^{2/3}}{x}",1,"(Csc[a + b*x^2]^2*(-1 + Cos[2*(a + b*x^2)] + 2*Sqrt[b]*Sqrt[Pi]*x*Cos[2*a]*FresnelS[(2*Sqrt[b]*x)/Sqrt[Pi]] + 2*Sqrt[b]*Sqrt[Pi]*x*FresnelC[(2*Sqrt[b]*x)/Sqrt[Pi]]*Sin[2*a])*(c*Sin[a + b*x^2]^3)^(2/3))/(2*x)","A",1
349,1,79,161,0.1479346,"\int \frac{\left(c \sin ^3\left(a+b x^2\right)\right)^{2/3}}{x^3} \, dx","Integrate[(c*Sin[a + b*x^2]^3)^(2/3)/x^3,x]","\frac{\csc ^2\left(a+b x^2\right) \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3} \left(2 b x^2 \sin (2 a) \text{Ci}\left(2 b x^2\right)+2 b x^2 \cos (2 a) \text{Si}\left(2 b x^2\right)+\cos \left(2 \left(a+b x^2\right)\right)-1\right)}{4 x^2}","\frac{1}{2} b \sin (2 a) \text{Ci}\left(2 b x^2\right) \csc ^2\left(a+b x^2\right) \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3}+\frac{1}{2} b \cos (2 a) \text{Si}\left(2 b x^2\right) \csc ^2\left(a+b x^2\right) \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3}-\frac{\csc ^2\left(a+b x^2\right) \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3}}{4 x^2}+\frac{\cos \left(2 \left(a+b x^2\right)\right) \csc ^2\left(a+b x^2\right) \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3}}{4 x^2}",1,"(Csc[a + b*x^2]^2*(c*Sin[a + b*x^2]^3)^(2/3)*(-1 + Cos[2*(a + b*x^2)] + 2*b*x^2*CosIntegral[2*b*x^2]*Sin[2*a] + 2*b*x^2*Cos[2*a]*SinIntegral[2*b*x^2]))/(4*x^2)","A",1
350,1,194,217,0.8492393,"\int x^m \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3} \, dx","Integrate[x^m*(c*Sin[a + b*x^n]^3)^(2/3),x]","\frac{e^{-2 i a} 2^{-\frac{m+2 n+1}{n}} x^{m+1} \left(b^2 x^{2 n}\right)^{-\frac{m+1}{n}} \csc ^2\left(a+b x^n\right) \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3} \left(e^{2 i a} n 2^{\frac{m+n+1}{n}} \left(b^2 x^{2 n}\right)^{\frac{m+1}{n}}+e^{4 i a} (m+1) \left(i b x^n\right)^{\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},-2 i b x^n\right)+(m+1) \left(-i b x^n\right)^{\frac{m+1}{n}} \Gamma \left(\frac{m+1}{n},2 i b x^n\right)\right)}{(m+1) n}","\frac{x^{m+1} \csc ^2\left(a+b x^n\right) \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}}{2 (m+1)}+\frac{e^{2 i a} 2^{-\frac{m+2 n+1}{n}} x^{m+1} \left(-i b x^n\right)^{-\frac{m+1}{n}} \csc ^2\left(a+b x^n\right) \Gamma \left(\frac{m+1}{n},-2 i b x^n\right) \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}}{n}+\frac{e^{-2 i a} 2^{-\frac{m+2 n+1}{n}} x^{m+1} \left(i b x^n\right)^{-\frac{m+1}{n}} \csc ^2\left(a+b x^n\right) \Gamma \left(\frac{m+1}{n},2 i b x^n\right) \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}}{n}",1,"(x^(1 + m)*Csc[a + b*x^n]^2*(2^((1 + m + n)/n)*E^((2*I)*a)*n*(b^2*x^(2*n))^((1 + m)/n) + E^((4*I)*a)*(1 + m)*(I*b*x^n)^((1 + m)/n)*Gamma[(1 + m)/n, (-2*I)*b*x^n] + (1 + m)*((-I)*b*x^n)^((1 + m)/n)*Gamma[(1 + m)/n, (2*I)*b*x^n])*(c*Sin[a + b*x^n]^3)^(2/3))/(2^((1 + m + 2*n)/n)*E^((2*I)*a)*(1 + m)*n*(b^2*x^(2*n))^((1 + m)/n))","A",1
351,1,161,188,0.5422057,"\int x^3 \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3} \, dx","Integrate[x^3*(c*Sin[a + b*x^n]^3)^(2/3),x]","\frac{e^{-2 i a} 2^{-\frac{4}{n}-3} x^4 \left(b^2 x^{2 n}\right)^{-4/n} \csc ^2\left(a+b x^n\right) \left(e^{2 i a} 16^{\frac{1}{n}} n \left(b^2 x^{2 n}\right)^{4/n}+2 e^{4 i a} \left(i b x^n\right)^{4/n} \Gamma \left(\frac{4}{n},-2 i b x^n\right)+2 \left(-i b x^n\right)^{4/n} \Gamma \left(\frac{4}{n},2 i b x^n\right)\right) \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}}{n}","\frac{1}{8} x^4 \csc ^2\left(a+b x^n\right) \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}+\frac{e^{2 i a} 4^{-\frac{2}{n}-1} x^4 \left(-i b x^n\right)^{-4/n} \Gamma \left(\frac{4}{n},-2 i b x^n\right) \csc ^2\left(a+b x^n\right) \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}}{n}+\frac{e^{-2 i a} 4^{-\frac{2}{n}-1} x^4 \left(i b x^n\right)^{-4/n} \Gamma \left(\frac{4}{n},2 i b x^n\right) \csc ^2\left(a+b x^n\right) \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}}{n}",1,"(2^(-3 - 4/n)*x^4*Csc[a + b*x^n]^2*(16^n^(-1)*E^((2*I)*a)*n*(b^2*x^(2*n))^(4/n) + 2*E^((4*I)*a)*(I*b*x^n)^(4/n)*Gamma[4/n, (-2*I)*b*x^n] + 2*((-I)*b*x^n)^(4/n)*Gamma[4/n, (2*I)*b*x^n])*(c*Sin[a + b*x^n]^3)^(2/3))/(E^((2*I)*a)*n*(b^2*x^(2*n))^(4/n))","A",1
352,1,168,188,0.5607593,"\int x^2 \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3} \, dx","Integrate[x^2*(c*Sin[a + b*x^n]^3)^(2/3),x]","\frac{e^{-2 i a} 2^{-\frac{3}{n}-2} x^3 \left(b^2 x^{2 n}\right)^{-3/n} \csc ^2\left(a+b x^n\right) \left(e^{2 i a} 2^{\frac{n+3}{n}} n \left(b^2 x^{2 n}\right)^{3/n}+3 e^{4 i a} \left(i b x^n\right)^{3/n} \Gamma \left(\frac{3}{n},-2 i b x^n\right)+3 \left(-i b x^n\right)^{3/n} \Gamma \left(\frac{3}{n},2 i b x^n\right)\right) \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}}{3 n}","\frac{1}{6} x^3 \csc ^2\left(a+b x^n\right) \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}+\frac{e^{2 i a} 2^{-\frac{3}{n}-2} x^3 \left(-i b x^n\right)^{-3/n} \Gamma \left(\frac{3}{n},-2 i b x^n\right) \csc ^2\left(a+b x^n\right) \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}}{n}+\frac{e^{-2 i a} 2^{-\frac{3}{n}-2} x^3 \left(i b x^n\right)^{-3/n} \Gamma \left(\frac{3}{n},2 i b x^n\right) \csc ^2\left(a+b x^n\right) \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}}{n}",1,"(2^(-2 - 3/n)*x^3*Csc[a + b*x^n]^2*(2^((3 + n)/n)*E^((2*I)*a)*n*(b^2*x^(2*n))^(3/n) + 3*E^((4*I)*a)*(I*b*x^n)^(3/n)*Gamma[3/n, (-2*I)*b*x^n] + 3*((-I)*b*x^n)^(3/n)*Gamma[3/n, (2*I)*b*x^n])*(c*Sin[a + b*x^n]^3)^(2/3))/(3*E^((2*I)*a)*n*(b^2*x^(2*n))^(3/n))","A",1
353,1,160,188,0.5583151,"\int x \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3} \, dx","Integrate[x*(c*Sin[a + b*x^n]^3)^(2/3),x]","\frac{e^{-2 i a} 4^{-\frac{n+1}{n}} x^2 \left(b^2 x^{2 n}\right)^{-2/n} \csc ^2\left(a+b x^n\right) \left(e^{2 i a} 4^{\frac{1}{n}} n \left(b^2 x^{2 n}\right)^{2/n}+e^{4 i a} \left(i b x^n\right)^{2/n} \Gamma \left(\frac{2}{n},-2 i b x^n\right)+\left(-i b x^n\right)^{2/n} \Gamma \left(\frac{2}{n},2 i b x^n\right)\right) \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}}{n}","\frac{1}{4} x^2 \csc ^2\left(a+b x^n\right) \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}+\frac{e^{2 i a} 4^{-\frac{1}{n}-1} x^2 \left(-i b x^n\right)^{-2/n} \Gamma \left(\frac{2}{n},-2 i b x^n\right) \csc ^2\left(a+b x^n\right) \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}}{n}+\frac{e^{-2 i a} 4^{-\frac{1}{n}-1} x^2 \left(i b x^n\right)^{-2/n} \Gamma \left(\frac{2}{n},2 i b x^n\right) \csc ^2\left(a+b x^n\right) \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}}{n}",1,"(x^2*Csc[a + b*x^n]^2*(4^n^(-1)*E^((2*I)*a)*n*(b^2*x^(2*n))^(2/n) + E^((4*I)*a)*(I*b*x^n)^(2/n)*Gamma[2/n, (-2*I)*b*x^n] + ((-I)*b*x^n)^(2/n)*Gamma[2/n, (2*I)*b*x^n])*(c*Sin[a + b*x^n]^3)^(2/3))/(4^((1 + n)/n)*E^((2*I)*a)*n*(b^2*x^(2*n))^(2/n))","A",1
354,1,149,178,0.2677976,"\int \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3} \, dx","Integrate[(c*Sin[a + b*x^n]^3)^(2/3),x]","\frac{e^{-2 i a} 2^{-\frac{1}{n}-2} x \left(b^2 x^{2 n}\right)^{-1/n} \csc ^2\left(a+b x^n\right) \left(e^{2 i a} 2^{\frac{1}{n}+1} n \left(b^2 x^{2 n}\right)^{\frac{1}{n}}+e^{4 i a} \left(i b x^n\right)^{\frac{1}{n}} \Gamma \left(\frac{1}{n},-2 i b x^n\right)+\left(-i b x^n\right)^{\frac{1}{n}} \Gamma \left(\frac{1}{n},2 i b x^n\right)\right) \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}}{n}","\frac{1}{2} x \csc ^2\left(a+b x^n\right) \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}+\frac{e^{2 i a} 2^{-\frac{1}{n}-2} x \left(-i b x^n\right)^{-1/n} \Gamma \left(\frac{1}{n},-2 i b x^n\right) \csc ^2\left(a+b x^n\right) \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}}{n}+\frac{e^{-2 i a} 2^{-\frac{1}{n}-2} x \left(i b x^n\right)^{-1/n} \Gamma \left(\frac{1}{n},2 i b x^n\right) \csc ^2\left(a+b x^n\right) \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}}{n}",1,"(2^(-2 - n^(-1))*x*Csc[a + b*x^n]^2*(2^(1 + n^(-1))*E^((2*I)*a)*n*(b^2*x^(2*n))^n^(-1) + E^((4*I)*a)*(I*b*x^n)^n^(-1)*Gamma[n^(-1), (-2*I)*b*x^n] + ((-I)*b*x^n)^n^(-1)*Gamma[n^(-1), (2*I)*b*x^n])*(c*Sin[a + b*x^n]^3)^(2/3))/(E^((2*I)*a)*n*(b^2*x^(2*n))^n^(-1))","A",1
355,1,63,121,0.1418511,"\int \frac{\left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}}{x} \, dx","Integrate[(c*Sin[a + b*x^n]^3)^(2/3)/x,x]","\frac{\csc ^2\left(a+b x^n\right) \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3} \left(-\cos (2 a) \text{Ci}\left(2 b x^n\right)+\sin (2 a) \text{Si}\left(2 b x^n\right)+n \log (x)\right)}{2 n}","-\frac{\cos (2 a) \text{Ci}\left(2 b x^n\right) \csc ^2\left(a+b x^n\right) \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}}{2 n}+\frac{\sin (2 a) \text{Si}\left(2 b x^n\right) \csc ^2\left(a+b x^n\right) \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}}{2 n}+\frac{1}{2} \log (x) \csc ^2\left(a+b x^n\right) \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}",1,"(Csc[a + b*x^n]^2*(c*Sin[a + b*x^n]^3)^(2/3)*(-(Cos[2*a]*CosIntegral[2*b*x^n]) + n*Log[x] + Sin[2*a]*SinIntegral[2*b*x^n]))/(2*n)","A",1
356,1,125,180,0.3443467,"\int \frac{\left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}}{x^2} \, dx","Integrate[(c*Sin[a + b*x^n]^3)^(2/3)/x^2,x]","\frac{e^{-2 i a} \csc ^2\left(a+b x^n\right) \left(e^{4 i a} 2^{\frac{1}{n}} \left(-i b x^n\right)^{\frac{1}{n}} \Gamma \left(-\frac{1}{n},-2 i b x^n\right)-2 e^{2 i a} n+2^{\frac{1}{n}} \left(i b x^n\right)^{\frac{1}{n}} \Gamma \left(-\frac{1}{n},2 i b x^n\right)\right) \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}}{4 n x}","-\frac{\csc ^2\left(a+b x^n\right) \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}}{2 x}+\frac{e^{2 i a} 2^{\frac{1}{n}-2} \left(-i b x^n\right)^{\frac{1}{n}} \Gamma \left(-\frac{1}{n},-2 i b x^n\right) \csc ^2\left(a+b x^n\right) \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}}{n x}+\frac{e^{-2 i a} 2^{\frac{1}{n}-2} \left(i b x^n\right)^{\frac{1}{n}} \Gamma \left(-\frac{1}{n},2 i b x^n\right) \csc ^2\left(a+b x^n\right) \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}}{n x}",1,"(Csc[a + b*x^n]^2*(-2*E^((2*I)*a)*n + 2^n^(-1)*E^((4*I)*a)*((-I)*b*x^n)^n^(-1)*Gamma[-n^(-1), (-2*I)*b*x^n] + 2^n^(-1)*(I*b*x^n)^n^(-1)*Gamma[-n^(-1), (2*I)*b*x^n])*(c*Sin[a + b*x^n]^3)^(2/3))/(4*E^((2*I)*a)*n*x)","A",1
357,1,129,184,0.3580676,"\int \frac{\left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}}{x^3} \, dx","Integrate[(c*Sin[a + b*x^n]^3)^(2/3)/x^3,x]","\frac{e^{-2 i a} \csc ^2\left(a+b x^n\right) \left(e^{4 i a} 4^{\frac{1}{n}} \left(-i b x^n\right)^{2/n} \Gamma \left(-\frac{2}{n},-2 i b x^n\right)-e^{2 i a} n+4^{\frac{1}{n}} \left(i b x^n\right)^{2/n} \Gamma \left(-\frac{2}{n},2 i b x^n\right)\right) \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}}{4 n x^2}","-\frac{\csc ^2\left(a+b x^n\right) \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}}{4 x^2}+\frac{e^{2 i a} 4^{\frac{1}{n}-1} \left(-i b x^n\right)^{2/n} \Gamma \left(-\frac{2}{n},-2 i b x^n\right) \csc ^2\left(a+b x^n\right) \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}}{n x^2}+\frac{e^{-2 i a} 4^{\frac{1}{n}-1} \left(i b x^n\right)^{2/n} \Gamma \left(-\frac{2}{n},2 i b x^n\right) \csc ^2\left(a+b x^n\right) \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}}{n x^2}",1,"(Csc[a + b*x^n]^2*(-(E^((2*I)*a)*n) + 4^n^(-1)*E^((4*I)*a)*((-I)*b*x^n)^(2/n)*Gamma[-2/n, (-2*I)*b*x^n] + 4^n^(-1)*(I*b*x^n)^(2/n)*Gamma[-2/n, (2*I)*b*x^n])*(c*Sin[a + b*x^n]^3)^(2/3))/(4*E^((2*I)*a)*n*x^2)","A",1