1,1,57,0,0.0730884,"\int x^5 \left(a+b \sin \left(c+d x^2\right)\right) \, dx","Int[x^5*(a + b*Sin[c + d*x^2]),x]","\frac{a x^6}{6}+\frac{b x^2 \sin \left(c+d x^2\right)}{d^2}+\frac{b \cos \left(c+d x^2\right)}{d^3}-\frac{b x^4 \cos \left(c+d x^2\right)}{2 d}","\frac{a x^6}{6}+\frac{b x^2 \sin \left(c+d x^2\right)}{d^2}+\frac{b \cos \left(c+d x^2\right)}{d^3}-\frac{b x^4 \cos \left(c+d x^2\right)}{2 d}",1,"(a*x^6)/6 + (b*Cos[c + d*x^2])/d^3 - (b*x^4*Cos[c + d*x^2])/(2*d) + (b*x^2*Sin[c + d*x^2])/d^2","A",6,4,16,0.2500,1,"{14, 3379, 3296, 2638}"
2,1,44,0,0.0425759,"\int x^3 \left(a+b \sin \left(c+d x^2\right)\right) \, dx","Int[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",5,4,16,0.2500,1,"{14, 3379, 3296, 2637}"
3,1,25,0,0.0212534,"\int x \left(a+b \sin \left(c+d x^2\right)\right) \, dx","Int[x*(a + b*Sin[c + d*x^2]),x]","\frac{a x^2}{2}-\frac{b \cos \left(c+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 + d*x^2])/(2*d)","A",4,3,14,0.2143,1,"{14, 3379, 2638}"
4,1,31,0,0.0342408,"\int \frac{a+b \sin \left(c+d x^2\right)}{x} \, dx","Int[(a + b*Sin[c + d*x^2])/x,x]","a \log (x)+\frac{1}{2} b \sin (c) \text{CosIntegral}\left(d x^2\right)+\frac{1}{2} b \cos (c) \text{Si}\left(d x^2\right)","a \log (x)+\frac{1}{2} b \sin (c) \text{CosIntegral}\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])/2 + (b*Cos[c]*SinIntegral[d*x^2])/2","A",5,4,16,0.2500,1,"{14, 3377, 3376, 3375}"
5,1,53,0,0.0911441,"\int \frac{a+b \sin \left(c+d x^2\right)}{x^3} \, dx","Int[(a + b*Sin[c + d*x^2])/x^3,x]","-\frac{a}{2 x^2}+\frac{1}{2} b d \cos (c) \text{CosIntegral}\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}","-\frac{a}{2 x^2}+\frac{1}{2} b d \cos (c) \text{CosIntegral}\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,"-a/(2*x^2) + (b*d*Cos[c]*CosIntegral[d*x^2])/2 - (b*Sin[c + d*x^2])/(2*x^2) - (b*d*Sin[c]*SinIntegral[d*x^2])/2","A",7,6,16,0.3750,1,"{14, 3379, 3297, 3303, 3299, 3302}"
6,1,74,0,0.1253835,"\int \frac{a+b \sin \left(c+d x^2\right)}{x^5} \, dx","Int[(a + b*Sin[c + d*x^2])/x^5,x]","-\frac{a}{4 x^4}-\frac{1}{4} b d^2 \sin (c) \text{CosIntegral}\left(d x^2\right)-\frac{1}{4} b d^2 \cos (c) \text{Si}\left(d x^2\right)-\frac{b \sin \left(c+d x^2\right)}{4 x^4}-\frac{b d \cos \left(c+d x^2\right)}{4 x^2}","-\frac{a}{4 x^4}-\frac{1}{4} b d^2 \sin (c) \text{CosIntegral}\left(d x^2\right)-\frac{1}{4} b d^2 \cos (c) \text{Si}\left(d x^2\right)-\frac{b \sin \left(c+d x^2\right)}{4 x^4}-\frac{b d \cos \left(c+d x^2\right)}{4 x^2}",1,"-a/(4*x^4) - (b*d*Cos[c + d*x^2])/(4*x^2) - (b*d^2*CosIntegral[d*x^2]*Sin[c])/4 - (b*Sin[c + d*x^2])/(4*x^4) - (b*d^2*Cos[c]*SinIntegral[d*x^2])/4","A",8,6,16,0.3750,1,"{14, 3379, 3297, 3303, 3299, 3302}"
7,1,121,0,0.1340592,"\int x^4 \left(a+b \sin \left(c+d x^2\right)\right) \, dx","Int[x^4*(a + b*Sin[c + d*x^2]),x]","\frac{a x^5}{5}-\frac{3 \sqrt{\frac{\pi }{2}} b \sin (c) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{d} 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}","\frac{a x^5}{5}-\frac{3 \sqrt{\frac{\pi }{2}} b \sin (c) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{d} 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^3*Cos[c + d*x^2])/(2*d) - (3*b*Sqrt[Pi/2]*Cos[c]*FresnelS[Sqrt[d]*Sqrt[2/Pi]*x])/(4*d^(5/2)) - (3*b*Sqrt[Pi/2]*FresnelC[Sqrt[d]*Sqrt[2/Pi]*x]*Sin[c])/(4*d^(5/2)) + (3*b*x*Sin[c + d*x^2])/(4*d^2)","A",7,6,16,0.3750,1,"{14, 3385, 3386, 3353, 3352, 3351}"
8,1,102,0,0.068195,"\int x^2 \left(a+b \sin \left(c+d x^2\right)\right) \, dx","Int[x^2*(a + b*Sin[c + d*x^2]),x]","\frac{a x^3}{3}+\frac{\sqrt{\frac{\pi }{2}} b \cos (c) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{d} 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}","\frac{a x^3}{3}+\frac{\sqrt{\frac{\pi }{2}} b \cos (c) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{d} 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 + d*x^2])/(2*d) + (b*Sqrt[Pi/2]*Cos[c]*FresnelC[Sqrt[d]*Sqrt[2/Pi]*x])/(2*d^(3/2)) - (b*Sqrt[Pi/2]*FresnelS[Sqrt[d]*Sqrt[2/Pi]*x]*Sin[c])/(2*d^(3/2))","A",6,5,16,0.3125,1,"{14, 3385, 3354, 3352, 3351}"
9,1,74,0,0.042957,"\int \left(a+b \sin \left(c+d x^2\right)\right) \, dx","Int[a + b*Sin[c + d*x^2],x]","a x+\frac{\sqrt{\frac{\pi }{2}} b \sin (c) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{d} x\right)}{\sqrt{d}}+\frac{\sqrt{\frac{\pi }{2}} b \cos (c) S\left(\sqrt{d} \sqrt{\frac{2}{\pi }} x\right)}{\sqrt{d}}","a x+\frac{\sqrt{\frac{\pi }{2}} b \sin (c) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{d} 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])/Sqrt[d] + (b*Sqrt[Pi/2]*FresnelC[Sqrt[d]*Sqrt[2/Pi]*x]*Sin[c])/Sqrt[d]","A",4,3,12,0.2500,1,"{3353, 3352, 3351}"
10,1,88,0,0.0744913,"\int \frac{a+b \sin \left(c+d x^2\right)}{x^2} \, dx","Int[(a + b*Sin[c + d*x^2])/x^2,x]","-\frac{a}{x}+\sqrt{2 \pi } b \sqrt{d} \cos (c) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{d} 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}","-\frac{a}{x}+\sqrt{2 \pi } b \sqrt{d} \cos (c) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{d} 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*Sqrt[d]*Sqrt[2*Pi]*Cos[c]*FresnelC[Sqrt[d]*Sqrt[2/Pi]*x] - b*Sqrt[d]*Sqrt[2*Pi]*FresnelS[Sqrt[d]*Sqrt[2/Pi]*x]*Sin[c] - (b*Sin[c + d*x^2])/x","A",6,5,16,0.3125,1,"{14, 3387, 3354, 3352, 3351}"
11,1,114,0,0.0907686,"\int \frac{a+b \sin \left(c+d x^2\right)}{x^4} \, dx","Int[(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} \sin (c) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{d} 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{b \sin \left(c+d x^2\right)}{3 x^3}-\frac{2 b d \cos \left(c+d x^2\right)}{3 x}","-\frac{a}{3 x^3}-\frac{2}{3} \sqrt{2 \pi } b d^{3/2} \sin (c) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{d} 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{b \sin \left(c+d x^2\right)}{3 x^3}-\frac{2 b d \cos \left(c+d x^2\right)}{3 x}",1,"-a/(3*x^3) - (2*b*d*Cos[c + d*x^2])/(3*x) - (2*b*d^(3/2)*Sqrt[2*Pi]*Cos[c]*FresnelS[Sqrt[d]*Sqrt[2/Pi]*x])/3 - (2*b*d^(3/2)*Sqrt[2*Pi]*FresnelC[Sqrt[d]*Sqrt[2/Pi]*x]*Sin[c])/3 - (b*Sin[c + d*x^2])/(3*x^3)","A",7,6,16,0.3750,1,"{14, 3387, 3388, 3353, 3352, 3351}"
12,1,163,0,0.2469974,"\int x^5 \left(a+b \sin \left(c+d x^2\right)\right)^2 \, dx","Int[x^5*(a + b*Sin[c + d*x^2])^2,x]","\frac{a^2 x^6}{6}+\frac{2 a b x^2 \sin \left(c+d x^2\right)}{d^2}+\frac{2 a b \cos \left(c+d x^2\right)}{d^3}-\frac{a b x^4 \cos \left(c+d x^2\right)}{d}+\frac{b^2 x^2 \sin ^2\left(c+d x^2\right)}{4 d^2}+\frac{b^2 \sin \left(c+d x^2\right) \cos \left(c+d x^2\right)}{8 d^3}-\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}","\frac{a^2 x^6}{6}+\frac{2 a b x^2 \sin \left(c+d x^2\right)}{d^2}+\frac{2 a b \cos \left(c+d x^2\right)}{d^3}-\frac{a b x^4 \cos \left(c+d x^2\right)}{d}+\frac{b^2 x^2 \sin ^2\left(c+d x^2\right)}{4 d^2}+\frac{b^2 \sin \left(c+d x^2\right) \cos \left(c+d x^2\right)}{8 d^3}-\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,"-(b^2*x^2)/(8*d^2) + (a^2*x^6)/6 + (b^2*x^6)/12 + (2*a*b*Cos[c + d*x^2])/d^3 - (a*b*x^4*Cos[c + d*x^2])/d + (2*a*b*x^2*Sin[c + d*x^2])/d^2 + (b^2*Cos[c + d*x^2]*Sin[c + d*x^2])/(8*d^3) - (b^2*x^4*Cos[c + d*x^2]*Sin[c + d*x^2])/(4*d) + (b^2*x^2*Sin[c + d*x^2]^2)/(4*d^2)","A",10,8,18,0.4444,1,"{3379, 3317, 3296, 2638, 3311, 30, 2635, 8}"
13,1,102,0,0.1336262,"\int x^3 \left(a+b \sin \left(c+d x^2\right)\right)^2 \, dx","Int[x^3*(a + b*Sin[c + d*x^2])^2,x]","\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}","\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,"(a^2*x^4)/4 + (b^2*x^4)/8 - (a*b*x^2*Cos[c + d*x^2])/d + (a*b*Sin[c + d*x^2])/d^2 - (b^2*x^2*Cos[c + d*x^2]*Sin[c + d*x^2])/(4*d) + (b^2*Sin[c + d*x^2]^2)/(8*d^2)","A",7,6,18,0.3333,1,"{3379, 3317, 3296, 2637, 3310, 30}"
14,1,58,0,0.0485753,"\int x \left(a+b \sin \left(c+d x^2\right)\right)^2 \, dx","Int[x*(a + b*Sin[c + d*x^2])^2,x]","\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}","\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,"((2*a^2 + b^2)*x^2)/4 - (a*b*Cos[c + d*x^2])/d - (b^2*Cos[c + d*x^2]*Sin[c + d*x^2])/(4*d)","A",2,2,16,0.1250,1,"{3379, 2644}"
15,1,74,0,0.1054745,"\int \frac{\left(a+b \sin \left(c+d x^2\right)\right)^2}{x} \, dx","Int[(a + b*Sin[c + d*x^2])^2/x,x]","\frac{1}{2} \left(2 a^2+b^2\right) \log (x)+a b \sin (c) \text{CosIntegral}\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{CosIntegral}\left(2 d x^2\right)+\frac{1}{4} b^2 \sin (2 c) \text{Si}\left(2 d x^2\right)","\frac{1}{2} \left(2 a^2+b^2\right) \log (x)+a b \sin (c) \text{CosIntegral}\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{CosIntegral}\left(2 d x^2\right)+\frac{1}{4} b^2 \sin (2 c) \text{Si}\left(2 d x^2\right)",1,"-(b^2*Cos[2*c]*CosIntegral[2*d*x^2])/4 + ((2*a^2 + b^2)*Log[x])/2 + a*b*CosIntegral[d*x^2]*Sin[c] + a*b*Cos[c]*SinIntegral[d*x^2] + (b^2*Sin[2*c]*SinIntegral[2*d*x^2])/4","A",9,6,18,0.3333,1,"{3403, 6, 3378, 3376, 3375, 3377}"
16,1,115,0,0.2213338,"\int \frac{\left(a+b \sin \left(c+d x^2\right)\right)^2}{x^3} \, dx","Int[(a + b*Sin[c + d*x^2])^2/x^3,x]","-\frac{2 a^2+b^2}{4 x^2}+a b d \cos (c) \text{CosIntegral}\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{CosIntegral}\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}","-\frac{2 a^2+b^2}{4 x^2}+a b d \cos (c) \text{CosIntegral}\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{CosIntegral}\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)/(4*x^2) + (b^2*Cos[2*(c + d*x^2)])/(4*x^2) + a*b*d*Cos[c]*CosIntegral[d*x^2] + (b^2*d*CosIntegral[2*d*x^2]*Sin[2*c])/2 - (a*b*Sin[c + d*x^2])/x^2 - a*b*d*Sin[c]*SinIntegral[d*x^2] + (b^2*d*Cos[2*c]*SinIntegral[2*d*x^2])/2","A",13,8,18,0.4444,1,"{3403, 6, 3380, 3297, 3303, 3299, 3302, 3379}"
17,1,169,0,0.2901916,"\int \frac{\left(a+b \sin \left(c+d x^2\right)\right)^2}{x^5} \, dx","Int[(a + b*Sin[c + d*x^2])^2/x^5,x]","-\frac{2 a^2+b^2}{8 x^4}-\frac{1}{2} a b d^2 \sin (c) \text{CosIntegral}\left(d x^2\right)-\frac{1}{2} a b d^2 \cos (c) \text{Si}\left(d x^2\right)-\frac{a b \sin \left(c+d x^2\right)}{2 x^4}-\frac{a b d \cos \left(c+d x^2\right)}{2 x^2}+\frac{1}{2} b^2 d^2 \cos (2 c) \text{CosIntegral}\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}","-\frac{2 a^2+b^2}{8 x^4}-\frac{1}{2} a b d^2 \sin (c) \text{CosIntegral}\left(d x^2\right)-\frac{1}{2} a b d^2 \cos (c) \text{Si}\left(d x^2\right)-\frac{a b \sin \left(c+d x^2\right)}{2 x^4}-\frac{a b d \cos \left(c+d x^2\right)}{2 x^2}+\frac{1}{2} b^2 d^2 \cos (2 c) \text{CosIntegral}\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,"-(2*a^2 + b^2)/(8*x^4) - (a*b*d*Cos[c + d*x^2])/(2*x^2) + (b^2*Cos[2*(c + d*x^2)])/(8*x^4) + (b^2*d^2*Cos[2*c]*CosIntegral[2*d*x^2])/2 - (a*b*d^2*CosIntegral[d*x^2]*Sin[c])/2 - (a*b*Sin[c + d*x^2])/(2*x^4) - (b^2*d*Sin[2*(c + d*x^2)])/(4*x^2) - (a*b*d^2*Cos[c]*SinIntegral[d*x^2])/2 - (b^2*d^2*Sin[2*c]*SinIntegral[2*d*x^2])/2","A",15,8,18,0.4444,1,"{3403, 6, 3380, 3297, 3303, 3299, 3302, 3379}"
18,1,247,0,0.2417538,"\int x^4 \left(a+b \sin \left(c+d x^2\right)\right)^2 \, dx","Int[x^4*(a + b*Sin[c + d*x^2])^2,x]","\frac{1}{10} x^5 \left(2 a^2+b^2\right)-\frac{3 \sqrt{\frac{\pi }{2}} a b \sin (c) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{d} 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) \text{FresnelC}\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}","\frac{1}{10} x^5 \left(2 a^2+b^2\right)-\frac{3 \sqrt{\frac{\pi }{2}} a b \sin (c) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{d} 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) \text{FresnelC}\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,"((2*a^2 + b^2)*x^5)/10 - (a*b*x^3*Cos[c + d*x^2])/d - (3*b^2*x*Cos[2*c + 2*d*x^2])/(32*d^2) + (3*b^2*Sqrt[Pi]*Cos[2*c]*FresnelC[(2*Sqrt[d]*x)/Sqrt[Pi]])/(64*d^(5/2)) - (3*a*b*Sqrt[Pi/2]*Cos[c]*FresnelS[Sqrt[d]*Sqrt[2/Pi]*x])/(2*d^(5/2)) - (3*a*b*Sqrt[Pi/2]*FresnelC[Sqrt[d]*Sqrt[2/Pi]*x]*Sin[c])/(2*d^(5/2)) - (3*b^2*Sqrt[Pi]*FresnelS[(2*Sqrt[d]*x)/Sqrt[Pi]]*Sin[2*c])/(64*d^(5/2)) + (3*a*b*x*Sin[c + d*x^2])/(2*d^2) - (b^2*x^3*Sin[2*c + 2*d*x^2])/(8*d)","A",13,8,18,0.4444,1,"{3403, 6, 3386, 3385, 3354, 3352, 3351, 3353}"
19,1,198,0,0.1566297,"\int x^2 \left(a+b \sin \left(c+d x^2\right)\right)^2 \, dx","Int[x^2*(a + b*Sin[c + d*x^2])^2,x]","\frac{1}{6} x^3 \left(2 a^2+b^2\right)+\frac{\sqrt{\frac{\pi }{2}} a b \cos (c) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{d} 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) \text{FresnelC}\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}","\frac{1}{6} x^3 \left(2 a^2+b^2\right)+\frac{\sqrt{\frac{\pi }{2}} a b \cos (c) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{d} 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) \text{FresnelC}\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,"((2*a^2 + b^2)*x^3)/6 - (a*b*x*Cos[c + d*x^2])/d + (a*b*Sqrt[Pi/2]*Cos[c]*FresnelC[Sqrt[d]*Sqrt[2/Pi]*x])/d^(3/2) + (b^2*Sqrt[Pi]*Cos[2*c]*FresnelS[(2*Sqrt[d]*x)/Sqrt[Pi]])/(16*d^(3/2)) - (a*b*Sqrt[Pi/2]*FresnelS[Sqrt[d]*Sqrt[2/Pi]*x]*Sin[c])/d^(3/2) + (b^2*Sqrt[Pi]*FresnelC[(2*Sqrt[d]*x)/Sqrt[Pi]]*Sin[2*c])/(16*d^(3/2)) - (b^2*x*Sin[2*c + 2*d*x^2])/(8*d)","A",11,8,18,0.4444,1,"{3403, 6, 3386, 3353, 3352, 3351, 3385, 3354}"
20,1,153,0,0.1091628,"\int \left(a+b \sin \left(c+d x^2\right)\right)^2 \, dx","Int[(a + b*Sin[c + d*x^2])^2,x]","\frac{1}{2} x \left(2 a^2+b^2\right)+\frac{\sqrt{2 \pi } a b \sin (c) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{d} 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) \text{FresnelC}\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}}","\frac{1}{2} x \left(2 a^2+b^2\right)+\frac{\sqrt{2 \pi } a b \sin (c) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{d} 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) \text{FresnelC}\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,"((2*a^2 + b^2)*x)/2 - (b^2*Sqrt[Pi]*Cos[2*c]*FresnelC[(2*Sqrt[d]*x)/Sqrt[Pi]])/(4*Sqrt[d]) + (a*b*Sqrt[2*Pi]*Cos[c]*FresnelS[Sqrt[d]*Sqrt[2/Pi]*x])/Sqrt[d] + (a*b*Sqrt[2*Pi]*FresnelC[Sqrt[d]*Sqrt[2/Pi]*x]*Sin[c])/Sqrt[d] + (b^2*Sqrt[Pi]*FresnelS[(2*Sqrt[d]*x)/Sqrt[Pi]]*Sin[2*c])/(4*Sqrt[d])","A",8,5,14,0.3571,1,"{3357, 3354, 3352, 3351, 3353}"
21,1,187,0,0.1624297,"\int \frac{\left(a+b \sin \left(c+d x^2\right)\right)^2}{x^2} \, dx","Int[(a + b*Sin[c + d*x^2])^2/x^2,x]","-\frac{2 a^2+b^2}{2 x}+2 \sqrt{2 \pi } a b \sqrt{d} \cos (c) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{d} 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) \text{FresnelC}\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}","-\frac{2 a^2+b^2}{2 x}+2 \sqrt{2 \pi } a b \sqrt{d} \cos (c) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{d} 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) \text{FresnelC}\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)/(2*x) + (b^2*Cos[2*c + 2*d*x^2])/(2*x) + 2*a*b*Sqrt[d]*Sqrt[2*Pi]*Cos[c]*FresnelC[Sqrt[d]*Sqrt[2/Pi]*x] + b^2*Sqrt[d]*Sqrt[Pi]*Cos[2*c]*FresnelS[(2*Sqrt[d]*x)/Sqrt[Pi]] - 2*a*b*Sqrt[d]*Sqrt[2*Pi]*FresnelS[Sqrt[d]*Sqrt[2/Pi]*x]*Sin[c] + b^2*Sqrt[d]*Sqrt[Pi]*FresnelC[(2*Sqrt[d]*x)/Sqrt[Pi]]*Sin[2*c] - (2*a*b*Sin[c + d*x^2])/x","A",11,8,18,0.4444,1,"{3403, 6, 3388, 3353, 3352, 3351, 3387, 3354}"
22,1,239,0,0.1972804,"\int \frac{\left(a+b \sin \left(c+d x^2\right)\right)^2}{x^4} \, dx","Int[(a + b*Sin[c + d*x^2])^2/x^4,x]","-\frac{2 a^2+b^2}{6 x^3}-\frac{4}{3} \sqrt{2 \pi } a b d^{3/2} \sin (c) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{d} 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{2 a b \sin \left(c+d x^2\right)}{3 x^3}-\frac{4 a b d \cos \left(c+d x^2\right)}{3 x}+\frac{4}{3} \sqrt{\pi } b^2 d^{3/2} \cos (2 c) \text{FresnelC}\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}","-\frac{2 a^2+b^2}{6 x^3}-\frac{4}{3} \sqrt{2 \pi } a b d^{3/2} \sin (c) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{d} 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{2 a b \sin \left(c+d x^2\right)}{3 x^3}-\frac{4 a b d \cos \left(c+d x^2\right)}{3 x}+\frac{4}{3} \sqrt{\pi } b^2 d^{3/2} \cos (2 c) \text{FresnelC}\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,"-(2*a^2 + b^2)/(6*x^3) - (4*a*b*d*Cos[c + d*x^2])/(3*x) + (b^2*Cos[2*c + 2*d*x^2])/(6*x^3) + (4*b^2*d^(3/2)*Sqrt[Pi]*Cos[2*c]*FresnelC[(2*Sqrt[d]*x)/Sqrt[Pi]])/3 - (4*a*b*d^(3/2)*Sqrt[2*Pi]*Cos[c]*FresnelS[Sqrt[d]*Sqrt[2/Pi]*x])/3 - (4*a*b*d^(3/2)*Sqrt[2*Pi]*FresnelC[Sqrt[d]*Sqrt[2/Pi]*x]*Sin[c])/3 - (4*b^2*d^(3/2)*Sqrt[Pi]*FresnelS[(2*Sqrt[d]*x)/Sqrt[Pi]]*Sin[2*c])/3 - (2*a*b*Sin[c + d*x^2])/(3*x^3) - (2*b^2*d*Sin[2*c + 2*d*x^2])/(3*x)","A",13,8,18,0.4444,1,"{3403, 6, 3388, 3387, 3354, 3352, 3351, 3353}"
23,1,117,0,0.130316,"\int x^5 \sin ^3\left(a+b x^2\right) \, dx","Int[x^5*Sin[a + b*x^2]^3,x]","\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{\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^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}","\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{\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^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,"(7*Cos[a + b*x^2])/(9*b^3) - (x^4*Cos[a + b*x^2])/(3*b) - Cos[a + b*x^2]^3/(27*b^3) + (2*x^2*Sin[a + b*x^2])/(3*b^2) - (x^4*Cos[a + b*x^2]*Sin[a + b*x^2]^2)/(6*b) + (x^2*Sin[a + b*x^2]^3)/(9*b^2)","A",7,5,14,0.3571,1,"{3379, 3311, 3296, 2638, 2633}"
24,1,79,0,0.073866,"\int x^3 \sin ^3\left(a+b x^2\right) \, dx","Int[x^3*Sin[a + b*x^2]^3,x]","\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}","\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,"-(x^2*Cos[a + b*x^2])/(3*b) + Sin[a + b*x^2]/(3*b^2) - (x^2*Cos[a + b*x^2]*Sin[a + b*x^2]^2)/(6*b) + Sin[a + b*x^2]^3/(18*b^2)","A",4,4,14,0.2857,1,"{3379, 3310, 3296, 2637}"
25,1,33,0,0.0307496,"\int x \sin ^3\left(a+b x^2\right) \, dx","Int[x*Sin[a + b*x^2]^3,x]","\frac{\cos ^3\left(a+b x^2\right)}{6 b}-\frac{\cos \left(a+b x^2\right)}{2 b}","\frac{\cos ^3\left(a+b x^2\right)}{6 b}-\frac{\cos \left(a+b x^2\right)}{2 b}",1,"-Cos[a + b*x^2]/(2*b) + Cos[a + b*x^2]^3/(6*b)","A",3,2,12,0.1667,1,"{3379, 2633}"
26,1,55,0,0.0953006,"\int \frac{\sin ^3\left(a+b x^2\right)}{x} \, dx","Int[Sin[a + b*x^2]^3/x,x]","\frac{3}{8} \sin (a) \text{CosIntegral}\left(b x^2\right)-\frac{1}{8} \sin (3 a) \text{CosIntegral}\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)","\frac{3}{8} \sin (a) \text{CosIntegral}\left(b x^2\right)-\frac{1}{8} \sin (3 a) \text{CosIntegral}\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])/8 - (CosIntegral[3*b*x^2]*Sin[3*a])/8 + (3*Cos[a]*SinIntegral[b*x^2])/8 - (Cos[3*a]*SinIntegral[3*b*x^2])/8","A",8,4,14,0.2857,1,"{3403, 3377, 3376, 3375}"
27,1,91,0,0.2200501,"\int \frac{\sin ^3\left(a+b x^2\right)}{x^3} \, dx","Int[Sin[a + b*x^2]^3/x^3,x]","\frac{3}{8} b \cos (a) \text{CosIntegral}\left(b x^2\right)-\frac{3}{8} b \cos (3 a) \text{CosIntegral}\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}","\frac{3}{8} b \cos (a) \text{CosIntegral}\left(b x^2\right)-\frac{3}{8} b \cos (3 a) \text{CosIntegral}\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*Cos[a]*CosIntegral[b*x^2])/8 - (3*b*Cos[3*a]*CosIntegral[3*b*x^2])/8 - (3*Sin[a + b*x^2])/(8*x^2) + Sin[3*(a + b*x^2)]/(8*x^2) - (3*b*Sin[a]*SinIntegral[b*x^2])/8 + (3*b*Sin[3*a]*SinIntegral[3*b*x^2])/8","A",12,6,14,0.4286,1,"{3403, 3379, 3297, 3303, 3299, 3302}"
28,1,188,0,0.2248088,"\int x^2 \sin ^3\left(a+b x^2\right) \, dx","Int[x^2*Sin[a + b*x^2]^3,x]","\frac{3 \sqrt{\frac{\pi }{2}} \cos (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} x\right)}{8 b^{3/2}}-\frac{\sqrt{\frac{\pi }{6}} \cos (3 a) \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{b} 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}","\frac{3 \sqrt{\frac{\pi }{2}} \cos (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} x\right)}{8 b^{3/2}}-\frac{\sqrt{\frac{\pi }{6}} \cos (3 a) \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{b} 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,"(-3*x*Cos[a + b*x^2])/(8*b) + (x*Cos[3*a + 3*b*x^2])/(24*b) + (3*Sqrt[Pi/2]*Cos[a]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x])/(8*b^(3/2)) - (Sqrt[Pi/6]*Cos[3*a]*FresnelC[Sqrt[b]*Sqrt[6/Pi]*x])/(24*b^(3/2)) - (3*Sqrt[Pi/2]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x]*Sin[a])/(8*b^(3/2)) + (Sqrt[Pi/6]*FresnelS[Sqrt[b]*Sqrt[6/Pi]*x]*Sin[3*a])/(24*b^(3/2))","A",10,5,14,0.3571,1,"{3403, 3385, 3354, 3352, 3351}"
29,1,153,0,0.0818357,"\int \sin ^3\left(a+b x^2\right) \, dx","Int[Sin[a + b*x^2]^3,x]","\frac{3 \sqrt{\frac{\pi }{2}} \sin (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} x\right)}{4 \sqrt{b}}-\frac{\sqrt{\frac{\pi }{6}} \sin (3 a) \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{b} 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}}","\frac{3 \sqrt{\frac{\pi }{2}} \sin (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} x\right)}{4 \sqrt{b}}-\frac{\sqrt{\frac{\pi }{6}} \sin (3 a) \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{b} 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,"(3*Sqrt[Pi/2]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x])/(4*Sqrt[b]) - (Sqrt[Pi/6]*Cos[3*a]*FresnelS[Sqrt[b]*Sqrt[6/Pi]*x])/(4*Sqrt[b]) + (3*Sqrt[Pi/2]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x]*Sin[a])/(4*Sqrt[b]) - (Sqrt[Pi/6]*FresnelC[Sqrt[b]*Sqrt[6/Pi]*x]*Sin[3*a])/(4*Sqrt[b])","A",8,4,10,0.4000,1,"{3357, 3353, 3352, 3351}"
30,1,168,0,0.1458266,"\int \frac{\sin ^3\left(a+b x^2\right)}{x^2} \, dx","Int[Sin[a + b*x^2]^3/x^2,x]","\frac{3}{2} \sqrt{\frac{\pi }{2}} \sqrt{b} \cos (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} x\right)-\frac{1}{2} \sqrt{\frac{3 \pi }{2}} \sqrt{b} \cos (3 a) \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{b} 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}","\frac{3}{2} \sqrt{\frac{\pi }{2}} \sqrt{b} \cos (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} x\right)-\frac{1}{2} \sqrt{\frac{3 \pi }{2}} \sqrt{b} \cos (3 a) \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} \sqrt{b} 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[Pi/2]*Cos[a]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x])/2 - (Sqrt[b]*Sqrt[(3*Pi)/2]*Cos[3*a]*FresnelC[Sqrt[b]*Sqrt[6/Pi]*x])/2 - (3*Sqrt[b]*Sqrt[Pi/2]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x]*Sin[a])/2 + (Sqrt[b]*Sqrt[(3*Pi)/2]*FresnelS[Sqrt[b]*Sqrt[6/Pi]*x]*Sin[3*a])/2 - Sin[a + b*x^2]^3/x","A",9,5,14,0.3571,1,"{3393, 4574, 3354, 3352, 3351}"
31,1,71,0,0.0532944,"\int x^2 \sin ^3\left(x^2\right) \, dx","Int[x^2*Sin[x^2]^3,x]","\frac{3}{8} \sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} x\right)-\frac{1}{24} \sqrt{\frac{\pi }{6}} \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} x\right)-\frac{3}{8} x \cos \left(x^2\right)+\frac{1}{24} x \cos \left(3 x^2\right)","\frac{3}{8} \sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} x\right)-\frac{1}{24} \sqrt{\frac{\pi }{6}} \text{FresnelC}\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,"(-3*x*Cos[x^2])/8 + (x*Cos[3*x^2])/24 + (3*Sqrt[Pi/2]*FresnelC[Sqrt[2/Pi]*x])/8 - (Sqrt[Pi/6]*FresnelC[Sqrt[6/Pi]*x])/24","A",6,3,10,0.3000,1,"{3403, 3385, 3352}"
32,1,84,0,0.0776766,"\int x^4 \cos \left(x^2\right) \sin ^2\left(x^2\right) \, dx","Int[x^4*Cos[x^2]*Sin[x^2]^2,x]","-\frac{3}{16} \sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} x\right)+\frac{1}{48} \sqrt{\frac{\pi }{6}} \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} x\right)+\frac{1}{6} x^3 \sin ^3\left(x^2\right)+\frac{3}{16} x \cos \left(x^2\right)-\frac{1}{48} x \cos \left(3 x^2\right)","-\frac{3}{16} \sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} x\right)+\frac{1}{48} \sqrt{\frac{\pi }{6}} \text{FresnelC}\left(\sqrt{\frac{6}{\pi }} x\right)+\frac{1}{6} x^3 \sin ^3\left(x^2\right)-\frac{1}{12} x \cos ^3\left(x^2\right)+\frac{1}{4} x \cos \left(x^2\right)",1,"(3*x*Cos[x^2])/16 - (x*Cos[3*x^2])/48 - (3*Sqrt[Pi/2]*FresnelC[Sqrt[2/Pi]*x])/16 + (Sqrt[Pi/6]*FresnelC[Sqrt[6/Pi]*x])/48 + (x^3*Sin[x^2]^3)/6","A",7,4,14,0.2857,1,"{3443, 3403, 3385, 3352}"
33,1,67,0,0.0446329,"\int x \sin ^7\left(a+b x^2\right) \, dx","Int[x*Sin[a + b*x^2]^7,x]","\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}","\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,"-Cos[a + b*x^2]/(2*b) + Cos[a + b*x^2]^3/(2*b) - (3*Cos[a + b*x^2]^5)/(10*b) + Cos[a + b*x^2]^7/(14*b)","A",3,2,12,0.1667,1,"{3379, 2633}"
34,1,44,0,0.1000061,"\int \frac{\left(1+\sin \left(x^2\right)\right)^2}{x^3} \, dx","Int[(1 + Sin[x^2])^2/x^3,x]","\text{CosIntegral}\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}","\text{CosIntegral}\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/(4*x^2) + Cos[2*x^2]/(4*x^2) + CosIntegral[x^2] - Sin[x^2]/x^2 + SinIntegral[2*x^2]/2","A",8,6,12,0.5000,1,"{3403, 3380, 3297, 3299, 3379, 3302}"
35,1,362,0,0.8788219,"\int \frac{x^5}{a+b \sin \left(c+d x^2\right)} \, dx","Int[x^5/(a + b*Sin[c + d*x^2]),x]","-\frac{x^2 \text{PolyLog}\left(2,\frac{i b e^{i \left(c+d x^2\right)}}{a-\sqrt{a^2-b^2}}\right)}{d^2 \sqrt{a^2-b^2}}+\frac{x^2 \text{PolyLog}\left(2,\frac{i b e^{i \left(c+d x^2\right)}}{\sqrt{a^2-b^2}+a}\right)}{d^2 \sqrt{a^2-b^2}}-\frac{i \text{PolyLog}\left(3,\frac{i b e^{i \left(c+d x^2\right)}}{a-\sqrt{a^2-b^2}}\right)}{d^3 \sqrt{a^2-b^2}}+\frac{i \text{PolyLog}\left(3,\frac{i b e^{i \left(c+d x^2\right)}}{\sqrt{a^2-b^2}+a}\right)}{d^3 \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}}","-\frac{x^2 \text{PolyLog}\left(2,\frac{i b e^{i \left(c+d x^2\right)}}{a-\sqrt{a^2-b^2}}\right)}{d^2 \sqrt{a^2-b^2}}+\frac{x^2 \text{PolyLog}\left(2,\frac{i b e^{i \left(c+d x^2\right)}}{\sqrt{a^2-b^2}+a}\right)}{d^2 \sqrt{a^2-b^2}}-\frac{i \text{PolyLog}\left(3,\frac{i b e^{i \left(c+d x^2\right)}}{a-\sqrt{a^2-b^2}}\right)}{d^3 \sqrt{a^2-b^2}}+\frac{i \text{PolyLog}\left(3,\frac{i b e^{i \left(c+d x^2\right)}}{\sqrt{a^2-b^2}+a}\right)}{d^3 \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,"((-I/2)*x^4*Log[1 - (I*b*E^(I*(c + d*x^2)))/(a - Sqrt[a^2 - b^2])])/(Sqrt[a^2 - b^2]*d) + ((I/2)*x^4*Log[1 - (I*b*E^(I*(c + d*x^2)))/(a + Sqrt[a^2 - b^2])])/(Sqrt[a^2 - b^2]*d) - (x^2*PolyLog[2, (I*b*E^(I*(c + d*x^2)))/(a - Sqrt[a^2 - b^2])])/(Sqrt[a^2 - b^2]*d^2) + (x^2*PolyLog[2, (I*b*E^(I*(c + d*x^2)))/(a + Sqrt[a^2 - b^2])])/(Sqrt[a^2 - b^2]*d^2) - (I*PolyLog[3, (I*b*E^(I*(c + d*x^2)))/(a - Sqrt[a^2 - b^2])])/(Sqrt[a^2 - b^2]*d^3) + (I*PolyLog[3, (I*b*E^(I*(c + d*x^2)))/(a + Sqrt[a^2 - b^2])])/(Sqrt[a^2 - b^2]*d^3)","A",11,7,18,0.3889,1,"{3379, 3323, 2264, 2190, 2531, 2282, 6589}"
36,1,245,0,0.5141786,"\int \frac{x^3}{a+b \sin \left(c+d x^2\right)} \, dx","Int[x^3/(a + b*Sin[c + d*x^2]),x]","-\frac{\text{PolyLog}\left(2,\frac{i b e^{i \left(c+d x^2\right)}}{a-\sqrt{a^2-b^2}}\right)}{2 d^2 \sqrt{a^2-b^2}}+\frac{\text{PolyLog}\left(2,\frac{i b e^{i \left(c+d x^2\right)}}{\sqrt{a^2-b^2}+a}\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}}","-\frac{\text{PolyLog}\left(2,\frac{i b e^{i \left(c+d x^2\right)}}{a-\sqrt{a^2-b^2}}\right)}{2 d^2 \sqrt{a^2-b^2}}+\frac{\text{PolyLog}\left(2,\frac{i b e^{i \left(c+d x^2\right)}}{\sqrt{a^2-b^2}+a}\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/2)*x^2*Log[1 - (I*b*E^(I*(c + d*x^2)))/(a - Sqrt[a^2 - b^2])])/(Sqrt[a^2 - b^2]*d) + ((I/2)*x^2*Log[1 - (I*b*E^(I*(c + d*x^2)))/(a + Sqrt[a^2 - b^2])])/(Sqrt[a^2 - b^2]*d) - PolyLog[2, (I*b*E^(I*(c + d*x^2)))/(a - Sqrt[a^2 - b^2])]/(2*Sqrt[a^2 - b^2]*d^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",9,6,18,0.3333,1,"{3379, 3323, 2264, 2190, 2279, 2391}"
37,1,48,0,0.0690306,"\int \frac{x}{a+b \sin \left(c+d x^2\right)} \, dx","Int[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",4,4,16,0.2500,1,"{3379, 2660, 618, 204}"
38,0,0,0,0.0275942,"\int \frac{1}{x \left(a+b \sin \left(c+d x^2\right)\right)} \, dx","Int[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,"Defer[Int][1/(x*(a + b*Sin[c + d*x^2])), x]","A",0,0,0,0,-1,"{}"
39,0,0,0,0.0274094,"\int \frac{1}{x^3 \left(a+b \sin \left(c+d x^2\right)\right)} \, dx","Int[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,"Defer[Int][1/(x^3*(a + b*Sin[c + d*x^2])), x]","A",0,0,0,0,-1,"{}"
40,0,0,0,0.0288569,"\int \frac{x^2}{a+b \sin \left(c+d x^2\right)} \, dx","Int[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,"Defer[Int][x^2/(a + b*Sin[c + d*x^2]), x]","A",0,0,0,0,-1,"{}"
41,0,0,0,0.0052529,"\int \frac{1}{a+b \sin \left(c+d x^2\right)} \, dx","Int[(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,"Defer[Int][(a + b*Sin[c + d*x^2])^(-1), x]","A",0,0,0,0,-1,"{}"
42,0,0,0,0.0270504,"\int \frac{1}{x^2 \left(a+b \sin \left(c+d x^2\right)\right)} \, dx","Int[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,"Defer[Int][1/(x^2*(a + b*Sin[c + d*x^2])), x]","A",0,0,0,0,-1,"{}"
43,1,663,0,1.3018949,"\int \frac{x^5}{\left(a+b \sin \left(c+d x^2\right)\right)^2} \, dx","Int[x^5/(a + b*Sin[c + d*x^2])^2,x]","-\frac{a x^2 \text{PolyLog}\left(2,\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)^{3/2}}+\frac{a x^2 \text{PolyLog}\left(2,\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)^{3/2}}+\frac{i \text{PolyLog}\left(2,\frac{i b e^{i \left(c+d x^2\right)}}{a-\sqrt{a^2-b^2}}\right)}{d^3 \left(a^2-b^2\right)}+\frac{i \text{PolyLog}\left(2,\frac{i b e^{i \left(c+d x^2\right)}}{\sqrt{a^2-b^2}+a}\right)}{d^3 \left(a^2-b^2\right)}-\frac{i a \text{PolyLog}\left(3,\frac{i b e^{i \left(c+d x^2\right)}}{a-\sqrt{a^2-b^2}}\right)}{d^3 \left(a^2-b^2\right)^{3/2}}+\frac{i a \text{PolyLog}\left(3,\frac{i b e^{i \left(c+d x^2\right)}}{\sqrt{a^2-b^2}+a}\right)}{d^3 \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)}","-\frac{a x^2 \text{PolyLog}\left(2,\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)^{3/2}}+\frac{a x^2 \text{PolyLog}\left(2,\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)^{3/2}}+\frac{i \text{PolyLog}\left(2,\frac{i b e^{i \left(c+d x^2\right)}}{a-\sqrt{a^2-b^2}}\right)}{d^3 \left(a^2-b^2\right)}+\frac{i \text{PolyLog}\left(2,\frac{i b e^{i \left(c+d x^2\right)}}{\sqrt{a^2-b^2}+a}\right)}{d^3 \left(a^2-b^2\right)}-\frac{i a \text{PolyLog}\left(3,\frac{i b e^{i \left(c+d x^2\right)}}{a-\sqrt{a^2-b^2}}\right)}{d^3 \left(a^2-b^2\right)^{3/2}}+\frac{i a \text{PolyLog}\left(3,\frac{i b e^{i \left(c+d x^2\right)}}{\sqrt{a^2-b^2}+a}\right)}{d^3 \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/2)*x^4)/((a^2 - b^2)*d) - (x^2*Log[1 - (I*b*E^(I*(c + d*x^2)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)*d^2) - ((I/2)*a*x^4*Log[1 - (I*b*E^(I*(c + d*x^2)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*d) - (x^2*Log[1 - (I*b*E^(I*(c + d*x^2)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)*d^2) + ((I/2)*a*x^4*Log[1 - (I*b*E^(I*(c + d*x^2)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*d) + (I*PolyLog[2, (I*b*E^(I*(c + d*x^2)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)*d^3) - (a*x^2*PolyLog[2, (I*b*E^(I*(c + d*x^2)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*d^2) + (I*PolyLog[2, (I*b*E^(I*(c + d*x^2)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)*d^3) + (a*x^2*PolyLog[2, (I*b*E^(I*(c + d*x^2)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*d^2) - (I*a*PolyLog[3, (I*b*E^(I*(c + d*x^2)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*d^3) + (I*a*PolyLog[3, (I*b*E^(I*(c + d*x^2)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*d^3) + (b*x^4*Cos[c + d*x^2])/(2*(a^2 - b^2)*d*(a + b*Sin[c + d*x^2]))","A",19,11,18,0.6111,1,"{3379, 3324, 3323, 2264, 2190, 2531, 2282, 6589, 4519, 2279, 2391}"
44,1,324,0,0.5960756,"\int \frac{x^3}{\left(a+b \sin \left(c+d x^2\right)\right)^2} \, dx","Int[x^3/(a + b*Sin[c + d*x^2])^2,x]","-\frac{a \text{PolyLog}\left(2,\frac{i b e^{i \left(c+d x^2\right)}}{a-\sqrt{a^2-b^2}}\right)}{2 d^2 \left(a^2-b^2\right)^{3/2}}+\frac{a \text{PolyLog}\left(2,\frac{i b e^{i \left(c+d x^2\right)}}{\sqrt{a^2-b^2}+a}\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)}","-\frac{a \text{PolyLog}\left(2,\frac{i b e^{i \left(c+d x^2\right)}}{a-\sqrt{a^2-b^2}}\right)}{2 d^2 \left(a^2-b^2\right)^{3/2}}+\frac{a \text{PolyLog}\left(2,\frac{i b e^{i \left(c+d x^2\right)}}{\sqrt{a^2-b^2}+a}\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/2)*a*x^2*Log[1 - (I*b*E^(I*(c + d*x^2)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*d) + ((I/2)*a*x^2*Log[1 - (I*b*E^(I*(c + d*x^2)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*d) - Log[a + b*Sin[c + d*x^2]]/(2*(a^2 - b^2)*d^2) - (a*PolyLog[2, (I*b*E^(I*(c + d*x^2)))/(a - Sqrt[a^2 - b^2])])/(2*(a^2 - b^2)^(3/2)*d^2) + (a*PolyLog[2, (I*b*E^(I*(c + d*x^2)))/(a + Sqrt[a^2 - b^2])])/(2*(a^2 - b^2)^(3/2)*d^2) + (b*x^2*Cos[c + d*x^2])/(2*(a^2 - b^2)*d*(a + b*Sin[c + d*x^2]))","A",12,9,18,0.5000,1,"{3379, 3324, 3323, 2264, 2190, 2279, 2391, 2668, 31}"
45,1,91,0,0.1020286,"\int \frac{x}{\left(a+b \sin \left(c+d x^2\right)\right)^2} \, dx","Int[x/(a + b*Sin[c + d*x^2])^2,x]","\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)}","\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,"(a*ArcTan[(b + a*Tan[(c + d*x^2)/2])/Sqrt[a^2 - b^2]])/((a^2 - b^2)^(3/2)*d) + (b*Cos[c + d*x^2])/(2*(a^2 - b^2)*d*(a + b*Sin[c + d*x^2]))","A",6,6,16,0.3750,1,"{3379, 2664, 12, 2660, 618, 204}"
46,0,0,0,0.0463497,"\int \frac{1}{x \left(a+b \sin \left(c+d x^2\right)\right)^2} \, dx","Int[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,"Defer[Int][1/(x*(a + b*Sin[c + d*x^2])^2), x]","A",0,0,0,0,-1,"{}"
47,0,0,0,0.0275243,"\int \frac{1}{x^3 \left(a+b \sin \left(c+d x^2\right)\right)^2} \, dx","Int[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,"Defer[Int][1/(x^3*(a + b*Sin[c + d*x^2])^2), x]","A",0,0,0,0,-1,"{}"
48,0,0,0,0.027027,"\int \frac{x^2}{\left(a+b \sin \left(c+d x^2\right)\right)^2} \, dx","Int[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,"Defer[Int][x^2/(a + b*Sin[c + d*x^2])^2, x]","A",0,0,0,0,-1,"{}"
49,0,0,0,0.0065561,"\int \frac{1}{\left(a+b \sin \left(c+d x^2\right)\right)^2} \, dx","Int[(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,"Defer[Int][(a + b*Sin[c + d*x^2])^(-2), x]","A",0,0,0,0,-1,"{}"
50,0,0,0,0.0254166,"\int \frac{1}{x^2 \left(a+b \sin \left(c+d x^2\right)\right)^2} \, dx","Int[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,"Defer[Int][1/(x^2*(a + b*Sin[c + d*x^2])^2), x]","A",0,0,0,0,-1,"{}"
51,0,0,0,0.0267236,"\int (e x)^m \left(a+b \sin \left(c+d x^2\right)\right)^p \, dx","Int[(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,"Defer[Int][(e*x)^m*(a + b*Sin[c + d*x^2])^p, x]","A",0,0,0,0,-1,"{}"
52,1,444,0,0.4796032,"\int (e x)^m \left(a+b \sin \left(c+d x^2\right)\right)^3 \, dx","Int[(e*x)^m*(a + b*Sin[c + d*x^2])^3,x]","\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} \text{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} \text{Gamma}\left(\frac{m+1}{2},i d x^2\right)}{16 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} \text{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} \text{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} \text{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} \text{Gamma}\left(\frac{m+1}{2},3 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 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} \text{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} \text{Gamma}\left(\frac{m+1}{2},i d x^2\right)}{16 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} \text{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} \text{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} \text{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} \text{Gamma}\left(\frac{m+1}{2},3 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)}",1,"(a*(2*a^2 + 3*b^2)*(e*x)^(1 + m))/(2*e*(1 + m)) + (((3*I)/16)*b*(4*a^2 + b^2)*E^(I*c)*(e*x)^(1 + m)*((-I)*d*x^2)^((-1 - m)/2)*Gamma[(1 + m)/2, (-I)*d*x^2])/e - (((3*I)/16)*b*(4*a^2 + b^2)*(e*x)^(1 + m)*(I*d*x^2)^((-1 - m)/2)*Gamma[(1 + m)/2, I*d*x^2])/(e*E^(I*c)) + (3*2^(-7/2 - m/2)*a*b^2*E^((2*I)*c)*(e*x)^(1 + m)*((-I)*d*x^2)^((-1 - m)/2)*Gamma[(1 + m)/2, (-2*I)*d*x^2])/e + (3*2^(-7/2 - m/2)*a*b^2*(e*x)^(1 + m)*(I*d*x^2)^((-1 - m)/2)*Gamma[(1 + m)/2, (2*I)*d*x^2])/(e*E^((2*I)*c)) - ((I/16)*3^(-1/2 - m/2)*b^3*E^((3*I)*c)*(e*x)^(1 + m)*((-I)*d*x^2)^((-1 - m)/2)*Gamma[(1 + m)/2, (-3*I)*d*x^2])/e + ((I/16)*3^(-1/2 - m/2)*b^3*(e*x)^(1 + m)*(I*d*x^2)^((-1 - m)/2)*Gamma[(1 + m)/2, (3*I)*d*x^2])/(e*E^((3*I)*c))","A",13,5,20,0.2500,1,"{3403, 6, 3390, 2218, 3389}"
53,1,279,0,0.2630995,"\int (e x)^m \left(a+b \sin \left(c+d x^2\right)\right)^2 \, dx","Int[(e*x)^m*(a + b*Sin[c + d*x^2])^2,x]","\frac{i a b e^{i c} \left(-i d x^2\right)^{\frac{1}{2} (-m-1)} (e x)^{m+1} \text{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} \text{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} \text{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} \text{Gamma}\left(\frac{m+1}{2},2 i d x^2\right)}{e}+\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} \text{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} \text{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} \text{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} \text{Gamma}\left(\frac{m+1}{2},2 i d x^2\right)}{e}+\frac{\left(2 a^2+b^2\right) (e x)^{m+1}}{2 e (m+1)}",1,"((2*a^2 + b^2)*(e*x)^(1 + m))/(2*e*(1 + m)) + ((I/2)*a*b*E^(I*c)*(e*x)^(1 + m)*((-I)*d*x^2)^((-1 - m)/2)*Gamma[(1 + m)/2, (-I)*d*x^2])/e - ((I/2)*a*b*(e*x)^(1 + m)*(I*d*x^2)^((-1 - m)/2)*Gamma[(1 + m)/2, I*d*x^2])/(e*E^(I*c)) + (2^(-7/2 - m/2)*b^2*E^((2*I)*c)*(e*x)^(1 + m)*((-I)*d*x^2)^((-1 - m)/2)*Gamma[(1 + m)/2, (-2*I)*d*x^2])/e + (2^(-7/2 - m/2)*b^2*(e*x)^(1 + m)*(I*d*x^2)^((-1 - m)/2)*Gamma[(1 + m)/2, (2*I)*d*x^2])/(e*E^((2*I)*c))","A",9,5,20,0.2500,1,"{3403, 6, 3390, 2218, 3389}"
54,1,134,0,0.1186722,"\int (e x)^m \left(a+b \sin \left(c+d x^2\right)\right) \, dx","Int[(e*x)^m*(a + b*Sin[c + d*x^2]),x]","\frac{i b e^{i c} \left(-i d x^2\right)^{\frac{1}{2} (-m-1)} (e x)^{m+1} \text{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} \text{Gamma}\left(\frac{m+1}{2},i d x^2\right)}{4 e}+\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} \text{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} \text{Gamma}\left(\frac{m+1}{2},i d x^2\right)}{4 e}+\frac{a (e x)^{m+1}}{e (m+1)}",1,"(a*(e*x)^(1 + m))/(e*(1 + m)) + ((I/4)*b*E^(I*c)*(e*x)^(1 + m)*((-I)*d*x^2)^((-1 - m)/2)*Gamma[(1 + m)/2, (-I)*d*x^2])/e - ((I/4)*b*(e*x)^(1 + m)*(I*d*x^2)^((-1 - m)/2)*Gamma[(1 + m)/2, I*d*x^2])/(e*E^(I*c))","A",5,3,18,0.1667,1,"{14, 3389, 2218}"
55,0,0,0,0.0277162,"\int \frac{(e x)^m}{a+b \sin \left(c+d x^2\right)} \, dx","Int[(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,"Defer[Int][(e*x)^m/(a + b*Sin[c + d*x^2]), x]","A",0,0,0,0,-1,"{}"
56,0,0,0,0.02626,"\int \frac{(e x)^m}{\left(a+b \sin \left(c+d x^2\right)\right)^2} \, dx","Int[(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,"Defer[Int][(e*x)^m/(a + b*Sin[c + d*x^2])^2, x]","A",0,0,0,0,-1,"{}"
57,1,44,0,0.0519132,"\int x^5 \left(a+b \sin \left(c+d x^3\right)\right) \, dx","Int[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",5,4,16,0.2500,1,"{14, 3379, 3296, 2637}"
58,1,25,0,0.0269652,"\int x^2 \left(a+b \sin \left(c+d x^3\right)\right) \, dx","Int[x^2*(a + b*Sin[c + d*x^3]),x]","\frac{a x^3}{3}-\frac{b \cos \left(c+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 + d*x^3])/(3*d)","A",4,3,16,0.1875,1,"{14, 3379, 2638}"
59,1,31,0,0.0387281,"\int \frac{a+b \sin \left(c+d x^3\right)}{x} \, dx","Int[(a + b*Sin[c + d*x^3])/x,x]","a \log (x)+\frac{1}{3} b \sin (c) \text{CosIntegral}\left(d x^3\right)+\frac{1}{3} b \cos (c) \text{Si}\left(d x^3\right)","a \log (x)+\frac{1}{3} b \sin (c) \text{CosIntegral}\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])/3 + (b*Cos[c]*SinIntegral[d*x^3])/3","A",5,4,16,0.2500,1,"{14, 3377, 3376, 3375}"
60,1,53,0,0.1015234,"\int \frac{a+b \sin \left(c+d x^3\right)}{x^4} \, dx","Int[(a + b*Sin[c + d*x^3])/x^4,x]","-\frac{a}{3 x^3}+\frac{1}{3} b d \cos (c) \text{CosIntegral}\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}","-\frac{a}{3 x^3}+\frac{1}{3} b d \cos (c) \text{CosIntegral}\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,"-a/(3*x^3) + (b*d*Cos[c]*CosIntegral[d*x^3])/3 - (b*Sin[c + d*x^3])/(3*x^3) - (b*d*Sin[c]*SinIntegral[d*x^3])/3","A",7,6,16,0.3750,1,"{14, 3379, 3297, 3303, 3299, 3302}"
61,1,112,0,0.085472,"\int x^4 \left(a+b \sin \left(c+d x^3\right)\right) \, dx","Int[x^4*(a + b*Sin[c + d*x^3]),x]","-\frac{b e^{i c} x^2 \text{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 \text{Gamma}\left(\frac{2}{3},i d x^3\right)}{9 d \left(i d x^3\right)^{2/3}}+\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 \text{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 \text{Gamma}\left(\frac{2}{3},i d x^3\right)}{9 d \left(i d x^3\right)^{2/3}}+\frac{a x^5}{5}-\frac{b x^2 \cos \left(c+d x^3\right)}{3 d}",1,"(a*x^5)/5 - (b*x^2*Cos[c + d*x^3])/(3*d) - (b*E^(I*c)*x^2*Gamma[2/3, (-I)*d*x^3])/(9*d*((-I)*d*x^3)^(2/3)) - (b*x^2*Gamma[2/3, I*d*x^3])/(9*d*E^(I*c)*(I*d*x^3)^(2/3))","A",6,4,16,0.2500,1,"{14, 3385, 3390, 2218}"
62,1,91,0,0.0642006,"\int x \left(a+b \sin \left(c+d x^3\right)\right) \, dx","Int[x*(a + b*Sin[c + d*x^3]),x]","\frac{i b e^{i c} x^2 \text{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 \text{Gamma}\left(\frac{2}{3},i d x^3\right)}{6 \left(i d x^3\right)^{2/3}}+\frac{a x^2}{2}","\frac{i b e^{i c} x^2 \text{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 \text{Gamma}\left(\frac{2}{3},i d x^3\right)}{6 \left(i d x^3\right)^{2/3}}+\frac{a x^2}{2}",1,"(a*x^2)/2 + ((I/6)*b*E^(I*c)*x^2*Gamma[2/3, (-I)*d*x^3])/((-I)*d*x^3)^(2/3) - ((I/6)*b*x^2*Gamma[2/3, I*d*x^3])/(E^(I*c)*(I*d*x^3)^(2/3))","A",5,3,14,0.2143,1,"{14, 3389, 2218}"
63,1,101,0,0.0780452,"\int \frac{a+b \sin \left(c+d x^3\right)}{x^2} \, dx","Int[(a + b*Sin[c + d*x^3])/x^2,x]","-\frac{b e^{i c} d x^2 \text{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 \text{Gamma}\left(\frac{2}{3},i d x^3\right)}{2 \left(i d x^3\right)^{2/3}}-\frac{a}{x}-\frac{b \sin \left(c+d x^3\right)}{x}","-\frac{b e^{i c} d x^2 \text{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 \text{Gamma}\left(\frac{2}{3},i d x^3\right)}{2 \left(i d x^3\right)^{2/3}}-\frac{a}{x}-\frac{b \sin \left(c+d x^3\right)}{x}",1,"-(a/x) - (b*d*E^(I*c)*x^2*Gamma[2/3, (-I)*d*x^3])/(2*((-I)*d*x^3)^(2/3)) - (b*d*x^2*Gamma[2/3, I*d*x^3])/(2*E^(I*c)*(I*d*x^3)^(2/3)) - (b*Sin[c + d*x^3])/x","A",6,4,16,0.2500,1,"{14, 3387, 3390, 2218}"
64,1,130,0,0.1016532,"\int \frac{a+b \sin \left(c+d x^3\right)}{x^5} \, dx","Int[(a + b*Sin[c + d*x^3])/x^5,x]","-\frac{3 i b e^{i c} d^2 x^2 \text{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 \text{Gamma}\left(\frac{2}{3},i d x^3\right)}{8 \left(i d x^3\right)^{2/3}}-\frac{a}{4 x^4}-\frac{b \sin \left(c+d x^3\right)}{4 x^4}-\frac{3 b d \cos \left(c+d x^3\right)}{4 x}","-\frac{3 i b e^{i c} d^2 x^2 \text{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 \text{Gamma}\left(\frac{2}{3},i d x^3\right)}{8 \left(i d x^3\right)^{2/3}}-\frac{a}{4 x^4}-\frac{b \sin \left(c+d x^3\right)}{4 x^4}-\frac{3 b d \cos \left(c+d x^3\right)}{4 x}",1,"-a/(4*x^4) - (3*b*d*Cos[c + d*x^3])/(4*x) - (((3*I)/8)*b*d^2*E^(I*c)*x^2*Gamma[2/3, (-I)*d*x^3])/((-I)*d*x^3)^(2/3) + (((3*I)/8)*b*d^2*x^2*Gamma[2/3, I*d*x^3])/(E^(I*c)*(I*d*x^3)^(2/3)) - (b*Sin[c + d*x^3])/(4*x^4)","A",7,5,16,0.3125,1,"{14, 3387, 3388, 3389, 2218}"
65,1,106,0,0.0723359,"\int x^3 \left(a+b \sin \left(c+d x^3\right)\right) \, dx","Int[x^3*(a + b*Sin[c + d*x^3]),x]","-\frac{b e^{i c} x \text{Gamma}\left(\frac{1}{3},-i d x^3\right)}{18 d \sqrt[3]{-i d x^3}}-\frac{b e^{-i c} x \text{Gamma}\left(\frac{1}{3},i d x^3\right)}{18 d \sqrt[3]{i d x^3}}+\frac{a x^4}{4}-\frac{b x \cos \left(c+d x^3\right)}{3 d}","-\frac{b e^{i c} x \text{Gamma}\left(\frac{1}{3},-i d x^3\right)}{18 d \sqrt[3]{-i d x^3}}-\frac{b e^{-i c} x \text{Gamma}\left(\frac{1}{3},i d x^3\right)}{18 d \sqrt[3]{i d x^3}}+\frac{a x^4}{4}-\frac{b x \cos \left(c+d x^3\right)}{3 d}",1,"(a*x^4)/4 - (b*x*Cos[c + d*x^3])/(3*d) - (b*E^(I*c)*x*Gamma[1/3, (-I)*d*x^3])/(18*d*((-I)*d*x^3)^(1/3)) - (b*x*Gamma[1/3, I*d*x^3])/(18*d*E^(I*c)*(I*d*x^3)^(1/3))","A",6,4,16,0.2500,1,"{14, 3385, 3356, 2208}"
66,1,82,0,0.0294216,"\int \left(a+b \sin \left(c+d x^3\right)\right) \, dx","Int[a + b*Sin[c + d*x^3],x]","\frac{i b e^{i c} x \text{Gamma}\left(\frac{1}{3},-i d x^3\right)}{6 \sqrt[3]{-i d x^3}}-\frac{i b e^{-i c} x \text{Gamma}\left(\frac{1}{3},i d x^3\right)}{6 \sqrt[3]{i d x^3}}+a x","\frac{i b e^{i c} x \text{Gamma}\left(\frac{1}{3},-i d x^3\right)}{6 \sqrt[3]{-i d x^3}}-\frac{i b e^{-i c} x \text{Gamma}\left(\frac{1}{3},i d x^3\right)}{6 \sqrt[3]{i d x^3}}+a x",1,"a*x + ((I/6)*b*E^(I*c)*x*Gamma[1/3, (-I)*d*x^3])/((-I)*d*x^3)^(1/3) - ((I/6)*b*x*Gamma[1/3, I*d*x^3])/(E^(I*c)*(I*d*x^3)^(1/3))","A",4,2,12,0.1667,1,"{3355, 2208}"
67,1,101,0,0.0549399,"\int \frac{a+b \sin \left(c+d x^3\right)}{x^3} \, dx","Int[(a + b*Sin[c + d*x^3])/x^3,x]","-\frac{b e^{i c} d x \text{Gamma}\left(\frac{1}{3},-i d x^3\right)}{4 \sqrt[3]{-i d x^3}}-\frac{b e^{-i c} d x \text{Gamma}\left(\frac{1}{3},i d x^3\right)}{4 \sqrt[3]{i d x^3}}-\frac{a}{2 x^2}-\frac{b \sin \left(c+d x^3\right)}{2 x^2}","-\frac{b e^{i c} d x \text{Gamma}\left(\frac{1}{3},-i d x^3\right)}{4 \sqrt[3]{-i d x^3}}-\frac{b e^{-i c} d x \text{Gamma}\left(\frac{1}{3},i d x^3\right)}{4 \sqrt[3]{i d x^3}}-\frac{a}{2 x^2}-\frac{b \sin \left(c+d x^3\right)}{2 x^2}",1,"-a/(2*x^2) - (b*d*E^(I*c)*x*Gamma[1/3, (-I)*d*x^3])/(4*((-I)*d*x^3)^(1/3)) - (b*d*x*Gamma[1/3, I*d*x^3])/(4*E^(I*c)*(I*d*x^3)^(1/3)) - (b*Sin[c + d*x^3])/(2*x^2)","A",6,4,16,0.2500,1,"{14, 3387, 3356, 2208}"
68,1,126,0,0.0711301,"\int \frac{a+b \sin \left(c+d x^3\right)}{x^6} \, dx","Int[(a + b*Sin[c + d*x^3])/x^6,x]","-\frac{3 i b e^{i c} d^2 x \text{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 \text{Gamma}\left(\frac{1}{3},i d x^3\right)}{20 \sqrt[3]{i d x^3}}-\frac{a}{5 x^5}-\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}","-\frac{3 i b e^{i c} d^2 x \text{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 \text{Gamma}\left(\frac{1}{3},i d x^3\right)}{20 \sqrt[3]{i d x^3}}-\frac{a}{5 x^5}-\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,"-a/(5*x^5) - (3*b*d*Cos[c + d*x^3])/(10*x^2) - (((3*I)/20)*b*d^2*E^(I*c)*x*Gamma[1/3, (-I)*d*x^3])/((-I)*d*x^3)^(1/3) + (((3*I)/20)*b*d^2*x*Gamma[1/3, I*d*x^3])/(E^(I*c)*(I*d*x^3)^(1/3)) - (b*Sin[c + d*x^3])/(5*x^5)","A",7,5,16,0.3125,1,"{14, 3387, 3388, 3355, 2208}"
69,1,107,0,0.1327652,"\int x^5 \left(a+b \sin \left(c+d x^3\right)\right)^2 \, dx","Int[x^5*(a + b*Sin[c + d*x^3])^2,x]","\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}","\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,"(a^2*x^6)/6 + (b^2*x^6)/12 - (2*a*b*x^3*Cos[c + d*x^3])/(3*d) + (2*a*b*Sin[c + d*x^3])/(3*d^2) - (b^2*x^3*Cos[c + d*x^3]*Sin[c + d*x^3])/(6*d) + (b^2*Sin[c + d*x^3]^2)/(12*d^2)","A",7,6,18,0.3333,1,"{3379, 3317, 3296, 2637, 3310, 30}"
70,1,60,0,0.0569236,"\int x^2 \left(a+b \sin \left(c+d x^3\right)\right)^2 \, dx","Int[x^2*(a + b*Sin[c + d*x^3])^2,x]","\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}","\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,"((2*a^2 + b^2)*x^3)/6 - (2*a*b*Cos[c + d*x^3])/(3*d) - (b^2*Cos[c + d*x^3]*Sin[c + d*x^3])/(6*d)","A",2,2,18,0.1111,1,"{3379, 2644}"
71,1,80,0,0.0927945,"\int \frac{\left(a+b \sin \left(c+d x^3\right)\right)^2}{x} \, dx","Int[(a + b*Sin[c + d*x^3])^2/x,x]","\frac{1}{2} \left(2 a^2+b^2\right) \log (x)+\frac{2}{3} a b \sin (c) \text{CosIntegral}\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{CosIntegral}\left(2 d x^3\right)+\frac{1}{6} b^2 \sin (2 c) \text{Si}\left(2 d x^3\right)","\frac{1}{2} \left(2 a^2+b^2\right) \log (x)+\frac{2}{3} a b \sin (c) \text{CosIntegral}\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{CosIntegral}\left(2 d x^3\right)+\frac{1}{6} b^2 \sin (2 c) \text{Si}\left(2 d x^3\right)",1,"-(b^2*Cos[2*c]*CosIntegral[2*d*x^3])/6 + ((2*a^2 + b^2)*Log[x])/2 + (2*a*b*CosIntegral[d*x^3]*Sin[c])/3 + (2*a*b*Cos[c]*SinIntegral[d*x^3])/3 + (b^2*Sin[2*c]*SinIntegral[2*d*x^3])/6","A",9,6,18,0.3333,1,"{3403, 6, 3378, 3376, 3375, 3377}"
72,1,122,0,0.2188413,"\int \frac{\left(a+b \sin \left(c+d x^3\right)\right)^2}{x^4} \, dx","Int[(a + b*Sin[c + d*x^3])^2/x^4,x]","-\frac{2 a^2+b^2}{6 x^3}+\frac{2}{3} a b d \cos (c) \text{CosIntegral}\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{CosIntegral}\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}","-\frac{2 a^2+b^2}{6 x^3}+\frac{2}{3} a b d \cos (c) \text{CosIntegral}\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{CosIntegral}\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)/(6*x^3) + (b^2*Cos[2*(c + d*x^3)])/(6*x^3) + (2*a*b*d*Cos[c]*CosIntegral[d*x^3])/3 + (b^2*d*CosIntegral[2*d*x^3]*Sin[2*c])/3 - (2*a*b*Sin[c + d*x^3])/(3*x^3) - (2*a*b*d*Sin[c]*SinIntegral[d*x^3])/3 + (b^2*d*Cos[2*c]*SinIntegral[2*d*x^3])/3","A",13,8,18,0.4444,1,"{3403, 6, 3380, 3297, 3303, 3299, 3302, 3379}"
73,1,249,0,0.2064651,"\int x^4 \left(a+b \sin \left(c+d x^3\right)\right)^2 \, dx","Int[x^4*(a + b*Sin[c + d*x^3])^2,x]","-\frac{2 a b e^{i c} x^2 \text{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 \text{Gamma}\left(\frac{2}{3},i d x^3\right)}{9 d \left(i d x^3\right)^{2/3}}+\frac{i b^2 e^{2 i c} x^2 \text{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 \text{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{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{b^2 x^2 \sin \left(2 c+2 d x^3\right)}{12 d}","-\frac{2 a b e^{i c} x^2 \text{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 \text{Gamma}\left(\frac{2}{3},i d x^3\right)}{9 d \left(i d x^3\right)^{2/3}}+\frac{i b^2 e^{2 i c} x^2 \text{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 \text{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{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{b^2 x^2 \sin \left(2 c+2 d x^3\right)}{12 d}",1,"((2*a^2 + b^2)*x^5)/10 - (2*a*b*x^2*Cos[c + d*x^3])/(3*d) - (2*a*b*E^(I*c)*x^2*Gamma[2/3, (-I)*d*x^3])/(9*d*((-I)*d*x^3)^(2/3)) - (2*a*b*x^2*Gamma[2/3, I*d*x^3])/(9*d*E^(I*c)*(I*d*x^3)^(2/3)) + ((I/36)*b^2*E^((2*I)*c)*x^2*Gamma[2/3, (-2*I)*d*x^3])/(2^(2/3)*d*((-I)*d*x^3)^(2/3)) - ((I/36)*b^2*x^2*Gamma[2/3, (2*I)*d*x^3])/(2^(2/3)*d*E^((2*I)*c)*(I*d*x^3)^(2/3)) - (b^2*x^2*Sin[2*c + 2*d*x^3])/(12*d)","A",11,7,18,0.3889,1,"{3403, 6, 3386, 3389, 2218, 3385, 3390}"
74,1,193,0,0.1359171,"\int x \left(a+b \sin \left(c+d x^3\right)\right)^2 \, dx","Int[x*(a + b*Sin[c + d*x^3])^2,x]","\frac{i a b e^{i c} x^2 \text{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 \text{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 \text{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 \text{Gamma}\left(\frac{2}{3},2 i d x^3\right)}{12\ 2^{2/3} \left(i d x^3\right)^{2/3}}+\frac{1}{4} x^2 \left(2 a^2+b^2\right)","\frac{i a b e^{i c} x^2 \text{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 \text{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 \text{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 \text{Gamma}\left(\frac{2}{3},2 i d x^3\right)}{12\ 2^{2/3} \left(i d x^3\right)^{2/3}}+\frac{1}{4} x^2 \left(2 a^2+b^2\right)",1,"((2*a^2 + b^2)*x^2)/4 + ((I/3)*a*b*E^(I*c)*x^2*Gamma[2/3, (-I)*d*x^3])/((-I)*d*x^3)^(2/3) - ((I/3)*a*b*x^2*Gamma[2/3, I*d*x^3])/(E^(I*c)*(I*d*x^3)^(2/3)) + (b^2*E^((2*I)*c)*x^2*Gamma[2/3, (-2*I)*d*x^3])/(12*2^(2/3)*((-I)*d*x^3)^(2/3)) + (b^2*x^2*Gamma[2/3, (2*I)*d*x^3])/(12*2^(2/3)*E^((2*I)*c)*(I*d*x^3)^(2/3))","A",9,5,16,0.3125,1,"{3403, 6, 3390, 2218, 3389}"
75,1,229,0,0.1892514,"\int \frac{\left(a+b \sin \left(c+d x^3\right)\right)^2}{x^2} \, dx","Int[(a + b*Sin[c + d*x^3])^2/x^2,x]","-\frac{a b e^{i c} d x^2 \text{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 \text{Gamma}\left(\frac{2}{3},i d x^3\right)}{\left(i d x^3\right)^{2/3}}+\frac{i b^2 e^{2 i c} d x^2 \text{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 \text{Gamma}\left(\frac{2}{3},2 i d x^3\right)}{2\ 2^{2/3} \left(i d x^3\right)^{2/3}}-\frac{2 a^2+b^2}{2 x}-\frac{2 a b \sin \left(c+d x^3\right)}{x}+\frac{b^2 \cos \left(2 c+2 d x^3\right)}{2 x}","-\frac{a b e^{i c} d x^2 \text{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 \text{Gamma}\left(\frac{2}{3},i d x^3\right)}{\left(i d x^3\right)^{2/3}}+\frac{i b^2 e^{2 i c} d x^2 \text{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 \text{Gamma}\left(\frac{2}{3},2 i d x^3\right)}{2\ 2^{2/3} \left(i d x^3\right)^{2/3}}-\frac{2 a^2+b^2}{2 x}-\frac{2 a b \sin \left(c+d x^3\right)}{x}+\frac{b^2 \cos \left(2 c+2 d x^3\right)}{2 x}",1,"-(2*a^2 + b^2)/(2*x) + (b^2*Cos[2*c + 2*d*x^3])/(2*x) - (a*b*d*E^(I*c)*x^2*Gamma[2/3, (-I)*d*x^3])/((-I)*d*x^3)^(2/3) - (a*b*d*x^2*Gamma[2/3, I*d*x^3])/(E^(I*c)*(I*d*x^3)^(2/3)) + ((I/2)*b^2*d*E^((2*I)*c)*x^2*Gamma[2/3, (-2*I)*d*x^3])/(2^(2/3)*((-I)*d*x^3)^(2/3)) - ((I/2)*b^2*d*x^2*Gamma[2/3, (2*I)*d*x^3])/(2^(2/3)*E^((2*I)*c)*(I*d*x^3)^(2/3)) - (2*a*b*Sin[c + d*x^3])/x","A",11,7,18,0.3889,1,"{3403, 6, 3388, 3389, 2218, 3387, 3390}"
76,1,283,0,0.2359462,"\int \frac{\left(a+b \sin \left(c+d x^3\right)\right)^2}{x^5} \, dx","Int[(a + b*Sin[c + d*x^3])^2/x^5,x]","-\frac{3 i a b e^{i c} d^2 x^2 \text{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 \text{Gamma}\left(\frac{2}{3},i d x^3\right)}{4 \left(i d x^3\right)^{2/3}}-\frac{3 b^2 e^{2 i c} d^2 x^2 \text{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 \text{Gamma}\left(\frac{2}{3},2 i d x^3\right)}{4\ 2^{2/3} \left(i d x^3\right)^{2/3}}-\frac{2 a^2+b^2}{8 x^4}-\frac{a b \sin \left(c+d x^3\right)}{2 x^4}-\frac{3 a b d \cos \left(c+d x^3\right)}{2 x}-\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}","-\frac{3 i a b e^{i c} d^2 x^2 \text{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 \text{Gamma}\left(\frac{2}{3},i d x^3\right)}{4 \left(i d x^3\right)^{2/3}}-\frac{3 b^2 e^{2 i c} d^2 x^2 \text{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 \text{Gamma}\left(\frac{2}{3},2 i d x^3\right)}{4\ 2^{2/3} \left(i d x^3\right)^{2/3}}-\frac{2 a^2+b^2}{8 x^4}-\frac{a b \sin \left(c+d x^3\right)}{2 x^4}-\frac{3 a b d \cos \left(c+d x^3\right)}{2 x}-\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,"-(2*a^2 + b^2)/(8*x^4) - (3*a*b*d*Cos[c + d*x^3])/(2*x) + (b^2*Cos[2*c + 2*d*x^3])/(8*x^4) - (((3*I)/4)*a*b*d^2*E^(I*c)*x^2*Gamma[2/3, (-I)*d*x^3])/((-I)*d*x^3)^(2/3) + (((3*I)/4)*a*b*d^2*x^2*Gamma[2/3, I*d*x^3])/(E^(I*c)*(I*d*x^3)^(2/3)) - (3*b^2*d^2*E^((2*I)*c)*x^2*Gamma[2/3, (-2*I)*d*x^3])/(4*2^(2/3)*((-I)*d*x^3)^(2/3)) - (3*b^2*d^2*x^2*Gamma[2/3, (2*I)*d*x^3])/(4*2^(2/3)*E^((2*I)*c)*(I*d*x^3)^(2/3)) - (a*b*Sin[c + d*x^3])/(2*x^4) - (3*b^2*d*Sin[2*c + 2*d*x^3])/(4*x)","A",13,7,18,0.3889,1,"{3403, 6, 3388, 3387, 3390, 2218, 3389}"
77,1,237,0,0.1502363,"\int x^3 \left(a+b \sin \left(c+d x^3\right)\right)^2 \, dx","Int[x^3*(a + b*Sin[c + d*x^3])^2,x]","-\frac{a b e^{i c} x \text{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 \text{Gamma}\left(\frac{1}{3},i d x^3\right)}{9 d \sqrt[3]{i d x^3}}+\frac{i b^2 e^{2 i c} x \text{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 \text{Gamma}\left(\frac{1}{3},2 i d x^3\right)}{72 \sqrt[3]{2} d \sqrt[3]{i d x^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{b^2 x \sin \left(2 c+2 d x^3\right)}{12 d}","-\frac{a b e^{i c} x \text{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 \text{Gamma}\left(\frac{1}{3},i d x^3\right)}{9 d \sqrt[3]{i d x^3}}+\frac{i b^2 e^{2 i c} x \text{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 \text{Gamma}\left(\frac{1}{3},2 i d x^3\right)}{72 \sqrt[3]{2} d \sqrt[3]{i d x^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{b^2 x \sin \left(2 c+2 d x^3\right)}{12 d}",1,"((2*a^2 + b^2)*x^4)/8 - (2*a*b*x*Cos[c + d*x^3])/(3*d) - (a*b*E^(I*c)*x*Gamma[1/3, (-I)*d*x^3])/(9*d*((-I)*d*x^3)^(1/3)) - (a*b*x*Gamma[1/3, I*d*x^3])/(9*d*E^(I*c)*(I*d*x^3)^(1/3)) + ((I/72)*b^2*E^((2*I)*c)*x*Gamma[1/3, (-2*I)*d*x^3])/(2^(1/3)*d*((-I)*d*x^3)^(1/3)) - ((I/72)*b^2*x*Gamma[1/3, (2*I)*d*x^3])/(2^(1/3)*d*E^((2*I)*c)*(I*d*x^3)^(1/3)) - (b^2*x*Sin[2*c + 2*d*x^3])/(12*d)","A",11,7,18,0.3889,1,"{3403, 6, 3386, 3355, 2208, 3385, 3356}"
78,1,183,0,0.0746712,"\int \left(a+b \sin \left(c+d x^3\right)\right)^2 \, dx","Int[(a + b*Sin[c + d*x^3])^2,x]","\frac{i a b e^{i c} x \text{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 \text{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 \text{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 \text{Gamma}\left(\frac{1}{3},2 i d x^3\right)}{12 \sqrt[3]{2} \sqrt[3]{i d x^3}}+\frac{1}{2} x \left(2 a^2+b^2\right)","\frac{i a b e^{i c} x \text{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 \text{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 \text{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 \text{Gamma}\left(\frac{1}{3},2 i d x^3\right)}{12 \sqrt[3]{2} \sqrt[3]{i d x^3}}+\frac{1}{2} x \left(2 a^2+b^2\right)",1,"((2*a^2 + b^2)*x)/2 + ((I/3)*a*b*E^(I*c)*x*Gamma[1/3, (-I)*d*x^3])/((-I)*d*x^3)^(1/3) - ((I/3)*a*b*x*Gamma[1/3, I*d*x^3])/(E^(I*c)*(I*d*x^3)^(1/3)) + (b^2*E^((2*I)*c)*x*Gamma[1/3, (-2*I)*d*x^3])/(12*2^(1/3)*((-I)*d*x^3)^(1/3)) + (b^2*x*Gamma[1/3, (2*I)*d*x^3])/(12*2^(1/3)*E^((2*I)*c)*(I*d*x^3)^(1/3))","A",8,4,14,0.2857,1,"{3357, 3356, 2208, 3355}"
79,1,225,0,0.1339685,"\int \frac{\left(a+b \sin \left(c+d x^3\right)\right)^2}{x^3} \, dx","Int[(a + b*Sin[c + d*x^3])^2/x^3,x]","-\frac{a b e^{i c} d x \text{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 \text{Gamma}\left(\frac{1}{3},i d x^3\right)}{2 \sqrt[3]{i d x^3}}+\frac{i b^2 e^{2 i c} d x \text{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 \text{Gamma}\left(\frac{1}{3},2 i d x^3\right)}{4 \sqrt[3]{2} \sqrt[3]{i d x^3}}-\frac{2 a^2+b^2}{4 x^2}-\frac{a b \sin \left(c+d x^3\right)}{x^2}+\frac{b^2 \cos \left(2 c+2 d x^3\right)}{4 x^2}","-\frac{a b e^{i c} d x \text{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 \text{Gamma}\left(\frac{1}{3},i d x^3\right)}{2 \sqrt[3]{i d x^3}}+\frac{i b^2 e^{2 i c} d x \text{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 \text{Gamma}\left(\frac{1}{3},2 i d x^3\right)}{4 \sqrt[3]{2} \sqrt[3]{i d x^3}}-\frac{2 a^2+b^2}{4 x^2}-\frac{a b \sin \left(c+d x^3\right)}{x^2}+\frac{b^2 \cos \left(2 c+2 d x^3\right)}{4 x^2}",1,"-(2*a^2 + b^2)/(4*x^2) + (b^2*Cos[2*c + 2*d*x^3])/(4*x^2) - (a*b*d*E^(I*c)*x*Gamma[1/3, (-I)*d*x^3])/(2*((-I)*d*x^3)^(1/3)) - (a*b*d*x*Gamma[1/3, I*d*x^3])/(2*E^(I*c)*(I*d*x^3)^(1/3)) + ((I/4)*b^2*d*E^((2*I)*c)*x*Gamma[1/3, (-2*I)*d*x^3])/(2^(1/3)*((-I)*d*x^3)^(1/3)) - ((I/4)*b^2*d*x*Gamma[1/3, (2*I)*d*x^3])/(2^(1/3)*E^((2*I)*c)*(I*d*x^3)^(1/3)) - (a*b*Sin[c + d*x^3])/x^2","A",11,7,18,0.3889,1,"{3403, 6, 3388, 3355, 2208, 3387, 3356}"
80,1,275,0,0.1829913,"\int \frac{\left(a+b \sin \left(c+d x^3\right)\right)^2}{x^6} \, dx","Int[(a + b*Sin[c + d*x^3])^2/x^6,x]","-\frac{3 i a b e^{i c} d^2 x \text{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 \text{Gamma}\left(\frac{1}{3},i d x^3\right)}{10 \sqrt[3]{i d x^3}}-\frac{3 b^2 e^{2 i c} d^2 x \text{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 \text{Gamma}\left(\frac{1}{3},2 i d x^3\right)}{10 \sqrt[3]{2} \sqrt[3]{i d x^3}}-\frac{2 a^2+b^2}{10 x^5}-\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 d \sin \left(2 c+2 d x^3\right)}{10 x^2}+\frac{b^2 \cos \left(2 c+2 d x^3\right)}{10 x^5}","-\frac{3 i a b e^{i c} d^2 x \text{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 \text{Gamma}\left(\frac{1}{3},i d x^3\right)}{10 \sqrt[3]{i d x^3}}-\frac{3 b^2 e^{2 i c} d^2 x \text{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 \text{Gamma}\left(\frac{1}{3},2 i d x^3\right)}{10 \sqrt[3]{2} \sqrt[3]{i d x^3}}-\frac{2 a^2+b^2}{10 x^5}-\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 d \sin \left(2 c+2 d x^3\right)}{10 x^2}+\frac{b^2 \cos \left(2 c+2 d x^3\right)}{10 x^5}",1,"-(2*a^2 + b^2)/(10*x^5) - (3*a*b*d*Cos[c + d*x^3])/(5*x^2) + (b^2*Cos[2*c + 2*d*x^3])/(10*x^5) - (((3*I)/10)*a*b*d^2*E^(I*c)*x*Gamma[1/3, (-I)*d*x^3])/((-I)*d*x^3)^(1/3) + (((3*I)/10)*a*b*d^2*x*Gamma[1/3, I*d*x^3])/(E^(I*c)*(I*d*x^3)^(1/3)) - (3*b^2*d^2*E^((2*I)*c)*x*Gamma[1/3, (-2*I)*d*x^3])/(10*2^(1/3)*((-I)*d*x^3)^(1/3)) - (3*b^2*d^2*x*Gamma[1/3, (2*I)*d*x^3])/(10*2^(1/3)*E^((2*I)*c)*(I*d*x^3)^(1/3)) - (2*a*b*Sin[c + d*x^3])/(5*x^5) - (3*b^2*d*Sin[2*c + 2*d*x^3])/(10*x^2)","A",13,7,18,0.3889,1,"{3403, 6, 3388, 3387, 3356, 2208, 3355}"
81,1,245,0,0.5027929,"\int \frac{x^5}{a+b \sin \left(c+d x^3\right)} \, dx","Int[x^5/(a + b*Sin[c + d*x^3]),x]","-\frac{\text{PolyLog}\left(2,\frac{i b e^{i \left(c+d x^3\right)}}{a-\sqrt{a^2-b^2}}\right)}{3 d^2 \sqrt{a^2-b^2}}+\frac{\text{PolyLog}\left(2,\frac{i b e^{i \left(c+d x^3\right)}}{\sqrt{a^2-b^2}+a}\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}}","-\frac{\text{PolyLog}\left(2,\frac{i b e^{i \left(c+d x^3\right)}}{a-\sqrt{a^2-b^2}}\right)}{3 d^2 \sqrt{a^2-b^2}}+\frac{\text{PolyLog}\left(2,\frac{i b e^{i \left(c+d x^3\right)}}{\sqrt{a^2-b^2}+a}\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/3)*x^3*Log[1 - (I*b*E^(I*(c + d*x^3)))/(a - Sqrt[a^2 - b^2])])/(Sqrt[a^2 - b^2]*d) + ((I/3)*x^3*Log[1 - (I*b*E^(I*(c + d*x^3)))/(a + Sqrt[a^2 - b^2])])/(Sqrt[a^2 - b^2]*d) - PolyLog[2, (I*b*E^(I*(c + d*x^3)))/(a - Sqrt[a^2 - b^2])]/(3*Sqrt[a^2 - b^2]*d^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",9,6,18,0.3333,1,"{3379, 3323, 2264, 2190, 2279, 2391}"
82,1,51,0,0.0778821,"\int \frac{x^2}{a+b \sin \left(c+d x^3\right)} \, dx","Int[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",4,4,18,0.2222,1,"{3379, 2660, 618, 204}"
83,0,0,0,0.0260812,"\int \frac{1}{x \left(a+b \sin \left(c+d x^3\right)\right)} \, dx","Int[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,"Defer[Int][1/(x*(a + b*Sin[c + d*x^3])), x]","A",0,0,0,0,-1,"{}"
84,0,0,0,0.0261377,"\int \frac{1}{x^4 \left(a+b \sin \left(c+d x^3\right)\right)} \, dx","Int[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,"Defer[Int][1/(x^4*(a + b*Sin[c + d*x^3])), x]","A",0,0,0,0,-1,"{}"
85,0,0,0,0.0146964,"\int \frac{x}{a+b \sin \left(c+d x^3\right)} \, dx","Int[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,"Defer[Int][x/(a + b*Sin[c + d*x^3]), x]","A",0,0,0,0,-1,"{}"
86,0,0,0,0.0257709,"\int \frac{1}{x^2 \left(a+b \sin \left(c+d x^3\right)\right)} \, dx","Int[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,"Defer[Int][1/(x^2*(a + b*Sin[c + d*x^3])), x]","A",0,0,0,0,-1,"{}"
87,0,0,0,0.0052006,"\int \frac{1}{a+b \sin \left(c+d x^3\right)} \, dx","Int[(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,"Defer[Int][(a + b*Sin[c + d*x^3])^(-1), x]","A",0,0,0,0,-1,"{}"
88,0,0,0,0.0256459,"\int \frac{1}{x^3 \left(a+b \sin \left(c+d x^3\right)\right)} \, dx","Int[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,"Defer[Int][1/(x^3*(a + b*Sin[c + d*x^3])), x]","A",0,0,0,0,-1,"{}"
89,1,324,0,0.5933498,"\int \frac{x^5}{\left(a+b \sin \left(c+d x^3\right)\right)^2} \, dx","Int[x^5/(a + b*Sin[c + d*x^3])^2,x]","-\frac{a \text{PolyLog}\left(2,\frac{i b e^{i \left(c+d x^3\right)}}{a-\sqrt{a^2-b^2}}\right)}{3 d^2 \left(a^2-b^2\right)^{3/2}}+\frac{a \text{PolyLog}\left(2,\frac{i b e^{i \left(c+d x^3\right)}}{\sqrt{a^2-b^2}+a}\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)}","-\frac{a \text{PolyLog}\left(2,\frac{i b e^{i \left(c+d x^3\right)}}{a-\sqrt{a^2-b^2}}\right)}{3 d^2 \left(a^2-b^2\right)^{3/2}}+\frac{a \text{PolyLog}\left(2,\frac{i b e^{i \left(c+d x^3\right)}}{\sqrt{a^2-b^2}+a}\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/3)*a*x^3*Log[1 - (I*b*E^(I*(c + d*x^3)))/(a - Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*d) + ((I/3)*a*x^3*Log[1 - (I*b*E^(I*(c + d*x^3)))/(a + Sqrt[a^2 - b^2])])/((a^2 - b^2)^(3/2)*d) - Log[a + b*Sin[c + d*x^3]]/(3*(a^2 - b^2)*d^2) - (a*PolyLog[2, (I*b*E^(I*(c + d*x^3)))/(a - Sqrt[a^2 - b^2])])/(3*(a^2 - b^2)^(3/2)*d^2) + (a*PolyLog[2, (I*b*E^(I*(c + d*x^3)))/(a + Sqrt[a^2 - b^2])])/(3*(a^2 - b^2)^(3/2)*d^2) + (b*x^3*Cos[c + d*x^3])/(3*(a^2 - b^2)*d*(a + b*Sin[c + d*x^3]))","A",12,9,18,0.5000,1,"{3379, 3324, 3323, 2264, 2190, 2279, 2391, 2668, 31}"
90,1,94,0,0.1085241,"\int \frac{x^2}{\left(a+b \sin \left(c+d x^3\right)\right)^2} \, dx","Int[x^2/(a + b*Sin[c + d*x^3])^2,x]","\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)}","\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]])/(3*(a^2 - b^2)^(3/2)*d) + (b*Cos[c + d*x^3])/(3*(a^2 - b^2)*d*(a + b*Sin[c + d*x^3]))","A",6,6,18,0.3333,1,"{3379, 2664, 12, 2660, 618, 204}"
91,0,0,0,0.0246425,"\int \frac{1}{x \left(a+b \sin \left(c+d x^3\right)\right)^2} \, dx","Int[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,"Defer[Int][1/(x*(a + b*Sin[c + d*x^3])^2), x]","A",0,0,0,0,-1,"{}"
92,0,0,0,0.0251098,"\int \frac{1}{x^4 \left(a+b \sin \left(c+d x^3\right)\right)^2} \, dx","Int[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,"Defer[Int][1/(x^4*(a + b*Sin[c + d*x^3])^2), x]","A",0,0,0,0,-1,"{}"
93,0,0,0,0.014517,"\int \frac{x}{\left(a+b \sin \left(c+d x^3\right)\right)^2} \, dx","Int[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,"Defer[Int][x/(a + b*Sin[c + d*x^3])^2, x]","A",0,0,0,0,-1,"{}"
94,0,0,0,0.0242327,"\int \frac{1}{x^2 \left(a+b \sin \left(c+d x^3\right)\right)^2} \, dx","Int[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,"Defer[Int][1/(x^2*(a + b*Sin[c + d*x^3])^2), x]","A",0,0,0,0,-1,"{}"
95,0,0,0,0.005102,"\int \frac{1}{\left(a+b \sin \left(c+d x^3\right)\right)^2} \, dx","Int[(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,"Defer[Int][(a + b*Sin[c + d*x^3])^(-2), x]","A",0,0,0,0,-1,"{}"
96,0,0,0,0.0246991,"\int \frac{1}{x^3 \left(a+b \sin \left(c+d x^3\right)\right)^2} \, dx","Int[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,"Defer[Int][1/(x^3*(a + b*Sin[c + d*x^3])^2), x]","A",0,0,0,0,-1,"{}"
97,0,0,0,0.0247014,"\int (e x)^m \left(a+b \sin \left(c+d x^3\right)\right)^p \, dx","Int[(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,"Defer[Int][(e*x)^m*(a + b*Sin[c + d*x^3])^p, x]","A",0,0,0,0,-1,"{}"
98,1,442,0,0.4143808,"\int (e x)^m \left(a+b \sin \left(c+d x^3\right)\right)^3 \, dx","Int[(e*x)^m*(a + b*Sin[c + d*x^3])^3,x]","\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} \text{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} \text{Gamma}\left(\frac{m+1}{3},i d x^3\right)}{8 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} \text{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} \text{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} \text{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} \text{Gamma}\left(\frac{m+1}{3},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{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} \text{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} \text{Gamma}\left(\frac{m+1}{3},i d x^3\right)}{8 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} \text{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} \text{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} \text{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} \text{Gamma}\left(\frac{m+1}{3},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)}",1,"(a*(2*a^2 + 3*b^2)*(e*x)^(1 + m))/(2*e*(1 + m)) + ((I/8)*b*(4*a^2 + b^2)*E^(I*c)*(e*x)^(1 + m)*((-I)*d*x^3)^((-1 - m)/3)*Gamma[(1 + m)/3, (-I)*d*x^3])/e - ((I/8)*b*(4*a^2 + b^2)*(e*x)^(1 + m)*(I*d*x^3)^((-1 - m)/3)*Gamma[(1 + m)/3, I*d*x^3])/(e*E^(I*c)) + (2^(-7/3 - m/3)*a*b^2*E^((2*I)*c)*(e*x)^(1 + m)*((-I)*d*x^3)^((-1 - m)/3)*Gamma[(1 + m)/3, (-2*I)*d*x^3])/e + (2^(-7/3 - m/3)*a*b^2*(e*x)^(1 + m)*(I*d*x^3)^((-1 - m)/3)*Gamma[(1 + m)/3, (2*I)*d*x^3])/(e*E^((2*I)*c)) - ((I/8)*3^(-4/3 - m/3)*b^3*E^((3*I)*c)*(e*x)^(1 + m)*((-I)*d*x^3)^((-1 - m)/3)*Gamma[(1 + m)/3, (-3*I)*d*x^3])/e + ((I/8)*3^(-4/3 - m/3)*b^3*(e*x)^(1 + m)*(I*d*x^3)^((-1 - m)/3)*Gamma[(1 + m)/3, (3*I)*d*x^3])/(e*E^((3*I)*c))","A",13,5,20,0.2500,1,"{3403, 6, 3390, 2218, 3389}"
99,1,285,0,0.2324438,"\int (e x)^m \left(a+b \sin \left(c+d x^3\right)\right)^2 \, dx","Int[(e*x)^m*(a + b*Sin[c + d*x^3])^2,x]","\frac{i a b e^{i c} \left(-i d x^3\right)^{\frac{1}{3} (-m-1)} (e x)^{m+1} \text{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} \text{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} \text{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} \text{Gamma}\left(\frac{m+1}{3},2 i d x^3\right)}{3 e}+\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} \text{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} \text{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} \text{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} \text{Gamma}\left(\frac{m+1}{3},2 i d x^3\right)}{3 e}+\frac{\left(2 a^2+b^2\right) (e x)^{m+1}}{2 e (m+1)}",1,"((2*a^2 + b^2)*(e*x)^(1 + m))/(2*e*(1 + m)) + ((I/3)*a*b*E^(I*c)*(e*x)^(1 + m)*((-I)*d*x^3)^((-1 - m)/3)*Gamma[(1 + m)/3, (-I)*d*x^3])/e - ((I/3)*a*b*(e*x)^(1 + m)*(I*d*x^3)^((-1 - m)/3)*Gamma[(1 + m)/3, I*d*x^3])/(e*E^(I*c)) + (2^(-7/3 - m/3)*b^2*E^((2*I)*c)*(e*x)^(1 + m)*((-I)*d*x^3)^((-1 - m)/3)*Gamma[(1 + m)/3, (-2*I)*d*x^3])/(3*e) + (2^(-7/3 - m/3)*b^2*(e*x)^(1 + m)*(I*d*x^3)^((-1 - m)/3)*Gamma[(1 + m)/3, (2*I)*d*x^3])/(3*e*E^((2*I)*c))","A",9,5,20,0.2500,1,"{3403, 6, 3390, 2218, 3389}"
100,1,134,0,0.0995589,"\int (e x)^m \left(a+b \sin \left(c+d x^3\right)\right) \, dx","Int[(e*x)^m*(a + b*Sin[c + d*x^3]),x]","\frac{i b e^{i c} \left(-i d x^3\right)^{\frac{1}{3} (-m-1)} (e x)^{m+1} \text{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} \text{Gamma}\left(\frac{m+1}{3},i d x^3\right)}{6 e}+\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} \text{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} \text{Gamma}\left(\frac{m+1}{3},i d x^3\right)}{6 e}+\frac{a (e x)^{m+1}}{e (m+1)}",1,"(a*(e*x)^(1 + m))/(e*(1 + m)) + ((I/6)*b*E^(I*c)*(e*x)^(1 + m)*((-I)*d*x^3)^((-1 - m)/3)*Gamma[(1 + m)/3, (-I)*d*x^3])/e - ((I/6)*b*(e*x)^(1 + m)*(I*d*x^3)^((-1 - m)/3)*Gamma[(1 + m)/3, I*d*x^3])/(e*E^(I*c))","A",5,3,18,0.1667,1,"{14, 3389, 2218}"
101,0,0,0,0.0264576,"\int \frac{(e x)^m}{a+b \sin \left(c+d x^3\right)} \, dx","Int[(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,"Defer[Int][(e*x)^m/(a + b*Sin[c + d*x^3]), x]","A",0,0,0,0,-1,"{}"
102,0,0,0,0.0246136,"\int \frac{(e x)^m}{\left(a+b \sin \left(c+d x^3\right)\right)^2} \, dx","Int[(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,"Defer[Int][(e*x)^m/(a + b*Sin[c + d*x^3])^2, x]","A",0,0,0,0,-1,"{}"
103,1,78,0,0.1313389,"\int x^2 \sin \left(a+\frac{b}{x}\right) \, dx","Int[x^2*Sin[a + b/x],x]","\frac{1}{6} b^3 \cos (a) \text{CosIntegral}\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)","\frac{1}{6} b^3 \cos (a) \text{CosIntegral}\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*x^2*Cos[a + b/x])/6 + (b^3*Cos[a]*CosIntegral[b/x])/6 - (b^2*x*Sin[a + b/x])/6 + (x^3*Sin[a + b/x])/3 - (b^3*Sin[a]*SinIntegral[b/x])/6","A",7,5,12,0.4167,1,"{3379, 3297, 3303, 3299, 3302}"
104,1,60,0,0.0976248,"\int x \sin \left(a+\frac{b}{x}\right) \, dx","Int[x*Sin[a + b/x],x]","\frac{1}{2} b^2 \sin (a) \text{CosIntegral}\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)","\frac{1}{2} b^2 \sin (a) \text{CosIntegral}\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*x*Cos[a + b/x])/2 + (b^2*CosIntegral[b/x]*Sin[a])/2 + (x^2*Sin[a + b/x])/2 + (b^2*Cos[a]*SinIntegral[b/x])/2","A",6,5,10,0.5000,1,"{3379, 3297, 3303, 3299, 3302}"
105,1,32,0,0.0722976,"\int \sin \left(a+\frac{b}{x}\right) \, dx","Int[Sin[a + b/x],x]","-b \cos (a) \text{CosIntegral}\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{CosIntegral}\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",5,5,8,0.6250,1,"{3361, 3297, 3303, 3299, 3302}"
106,1,21,0,0.0282507,"\int \frac{\sin \left(a+\frac{b}{x}\right)}{x} \, dx","Int[Sin[a + b/x]/x,x]","\sin (a) \left(-\text{CosIntegral}\left(\frac{b}{x}\right)\right)-\cos (a) \text{Si}\left(\frac{b}{x}\right)","\sin (a) \left(-\text{CosIntegral}\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",3,3,12,0.2500,1,"{3377, 3376, 3375}"
107,1,12,0,0.0138755,"\int \frac{\sin \left(a+\frac{b}{x}\right)}{x^2} \, dx","Int[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",2,2,12,0.1667,1,"{3379, 2638}"
108,1,29,0,0.0246476,"\int \frac{\sin \left(a+\frac{b}{x}\right)}{x^3} \, dx","Int[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",3,3,12,0.2500,1,"{3379, 3296, 2637}"
109,1,45,0,0.0462511,"\int \frac{\sin \left(a+\frac{b}{x}\right)}{x^4} \, dx","Int[Sin[a + b/x]/x^4,x]","-\frac{2 \sin \left(a+\frac{b}{x}\right)}{b^2 x}-\frac{2 \cos \left(a+\frac{b}{x}\right)}{b^3}+\frac{\cos \left(a+\frac{b}{x}\right)}{b x^2}","-\frac{2 \sin \left(a+\frac{b}{x}\right)}{b^2 x}-\frac{2 \cos \left(a+\frac{b}{x}\right)}{b^3}+\frac{\cos \left(a+\frac{b}{x}\right)}{b x^2}",1,"(-2*Cos[a + b/x])/b^3 + Cos[a + b/x]/(b*x^2) - (2*Sin[a + b/x])/(b^2*x)","A",4,3,12,0.2500,1,"{3379, 3296, 2638}"
110,1,61,0,0.0676861,"\int \frac{\sin \left(a+\frac{b}{x}\right)}{x^5} \, dx","Int[Sin[a + b/x]/x^5,x]","-\frac{3 \sin \left(a+\frac{b}{x}\right)}{b^2 x^2}+\frac{6 \sin \left(a+\frac{b}{x}\right)}{b^4}-\frac{6 \cos \left(a+\frac{b}{x}\right)}{b^3 x}+\frac{\cos \left(a+\frac{b}{x}\right)}{b x^3}","-\frac{3 \sin \left(a+\frac{b}{x}\right)}{b^2 x^2}+\frac{6 \sin \left(a+\frac{b}{x}\right)}{b^4}-\frac{6 \cos \left(a+\frac{b}{x}\right)}{b^3 x}+\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",5,3,12,0.2500,1,"{3379, 3296, 2637}"
111,1,97,0,0.1691477,"\int x^2 \sin ^2\left(a+\frac{b}{x}\right) \, dx","Int[x^2*Sin[a + b/x]^2,x]","\frac{2}{3} b^3 \sin (2 a) \text{CosIntegral}\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} b x^2 \sin \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{x^3}{6}","\frac{2}{3} b^3 \sin (2 a) \text{CosIntegral}\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} b x^2 \sin \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{x^3}{6}",1,"x^3/6 + (b^2*x*Cos[2*(a + b/x)])/3 - (x^3*Cos[2*(a + b/x)])/6 + (2*b^3*CosIntegral[(2*b)/x]*Sin[2*a])/3 + (b*x^2*Sin[2*(a + b/x)])/6 + (2*b^3*Cos[2*a]*SinIntegral[(2*b)/x])/3","A",9,6,14,0.4286,1,"{3425, 3380, 3297, 3303, 3299, 3302}"
112,1,65,0,0.1042189,"\int x \sin ^2\left(a+\frac{b}{x}\right) \, dx","Int[x*Sin[a + b/x]^2,x]","b^2 (-\cos (2 a)) \text{CosIntegral}\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)","b^2 (-\cos (2 a)) \text{CosIntegral}\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^2*Sin[a + b/x]^2)/2 + (b*x*Sin[2*(a + b/x)])/2 + b^2*Sin[2*a]*SinIntegral[(2*b)/x]","A",8,8,12,0.6667,1,"{3393, 4573, 3373, 3361, 3297, 3303, 3299, 3302}"
113,1,41,0,0.0905833,"\int \sin ^2\left(a+\frac{b}{x}\right) \, dx","Int[Sin[a + b/x]^2,x]","-b \sin (2 a) \text{CosIntegral}\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{CosIntegral}\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",6,6,10,0.6000,1,"{3361, 3313, 12, 3303, 3299, 3302}"
114,1,37,0,0.049541,"\int \frac{\sin ^2\left(a+\frac{b}{x}\right)}{x} \, dx","Int[Sin[a + b/x]^2/x,x]","\frac{1}{2} \cos (2 a) \text{CosIntegral}\left(\frac{2 b}{x}\right)-\frac{1}{2} \sin (2 a) \text{Si}\left(\frac{2 b}{x}\right)+\frac{\log (x)}{2}","\frac{1}{2} \cos (2 a) \text{CosIntegral}\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])/2 + Log[x]/2 - (Sin[2*a]*SinIntegral[(2*b)/x])/2","A",5,4,14,0.2857,1,"{3425, 3378, 3376, 3375}"
115,1,31,0,0.0268488,"\int \frac{\sin ^2\left(a+\frac{b}{x}\right)}{x^2} \, dx","Int[Sin[a + b/x]^2/x^2,x]","\frac{\sin \left(a+\frac{b}{x}\right) \cos \left(a+\frac{b}{x}\right)}{2 b}-\frac{1}{2 x}","\frac{\sin \left(a+\frac{b}{x}\right) \cos \left(a+\frac{b}{x}\right)}{2 b}-\frac{1}{2 x}",1,"-1/(2*x) + (Cos[a + b/x]*Sin[a + b/x])/(2*b)","A",3,3,14,0.2143,1,"{3379, 2635, 8}"
116,1,51,0,0.039533,"\int \frac{\sin ^2\left(a+\frac{b}{x}\right)}{x^3} \, dx","Int[Sin[a + b/x]^2/x^3,x]","-\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}","-\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,"-1/(4*x^2) + (Cos[a + b/x]*Sin[a + b/x])/(2*b*x) - Sin[a + b/x]^2/(4*b^2)","A",3,3,14,0.2143,1,"{3379, 3310, 30}"
117,1,87,0,0.0653922,"\int \frac{\sin ^2\left(a+\frac{b}{x}\right)}{x^4} \, dx","Int[Sin[a + b/x]^2/x^4,x]","-\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)}{4 b^3}+\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}","-\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)}{4 b^3}+\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,"-1/(6*x^3) + 1/(4*b^2*x) - (Cos[a + b/x]*Sin[a + b/x])/(4*b^3) + (Cos[a + b/x]*Sin[a + b/x])/(2*b*x^2) - Sin[a + b/x]^2/(2*b^2*x)","A",5,5,14,0.3571,1,"{3379, 3311, 30, 2635, 8}"
118,1,107,0,0.0807238,"\int \frac{\sin ^2\left(a+\frac{b}{x}\right)}{x^5} \, dx","Int[Sin[a + b/x]^2/x^5,x]","-\frac{3 \sin ^2\left(a+\frac{b}{x}\right)}{4 b^2 x^2}+\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{\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}","-\frac{3 \sin ^2\left(a+\frac{b}{x}\right)}{4 b^2 x^2}+\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{\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/(8*x^4) + 3/(8*b^2*x^2) + (Cos[a + b/x]*Sin[a + b/x])/(2*b*x^3) - (3*Cos[a + b/x]*Sin[a + b/x])/(4*b^3*x) + (3*Sin[a + b/x]^2)/(8*b^4) - (3*Sin[a + b/x]^2)/(4*b^2*x^2)","A",5,4,14,0.2857,1,"{3379, 3311, 30, 3310}"
119,1,80,0,0.0577005,"\int \sin \left(a+\frac{b}{x^2}\right) \, dx","Int[Sin[a + b/x^2],x]","\sqrt{2 \pi } \left(-\sqrt{b}\right) \cos (a) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{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)","\sqrt{2 \pi } \left(-\sqrt{b}\right) \cos (a) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{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,"-(Sqrt[b]*Sqrt[2*Pi]*Cos[a]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/x]) + Sqrt[b]*Sqrt[2*Pi]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/x]*Sin[a] + x*Sin[a + b/x^2]","A",5,5,8,0.6250,1,"{3359, 3387, 3354, 3352, 3351}"
120,1,25,0,0.0291302,"\int \frac{\sin \left(a+\frac{b}{x^2}\right)}{x} \, dx","Int[Sin[a + b/x^2]/x,x]","-\frac{1}{2} \sin (a) \text{CosIntegral}\left(\frac{b}{x^2}\right)-\frac{1}{2} \cos (a) \text{Si}\left(\frac{b}{x^2}\right)","-\frac{1}{2} \sin (a) \text{CosIntegral}\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])/2 - (Cos[a]*SinIntegral[b/x^2])/2","A",3,3,12,0.2500,1,"{3377, 3376, 3375}"
121,1,75,0,0.030979,"\int \frac{\sin \left(a+\frac{b}{x^2}\right)}{x^2} \, dx","Int[Sin[a + b/x^2]/x^2,x]","-\frac{\sqrt{\frac{\pi }{2}} \sin (a) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{x}\right)}{\sqrt{b}}-\frac{\sqrt{\frac{\pi }{2}} \cos (a) S\left(\frac{\sqrt{b} \sqrt{\frac{2}{\pi }}}{x}\right)}{\sqrt{b}}","-\frac{\sqrt{\frac{\pi }{2}} \sin (a) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{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])/Sqrt[b]) - (Sqrt[Pi/2]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/x]*Sin[a])/Sqrt[b]","A",4,4,12,0.3333,1,"{3383, 3353, 3352, 3351}"
122,1,15,0,0.0157894,"\int \frac{\sin \left(a+\frac{b}{x^2}\right)}{x^3} \, dx","Int[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",2,2,12,0.1667,1,"{3379, 2638}"
123,1,97,0,0.0585725,"\int \frac{\sin \left(a+\frac{b}{x^2}\right)}{x^4} \, dx","Int[Sin[a + b/x^2]/x^4,x]","-\frac{\sqrt{\frac{\pi }{2}} \cos (a) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{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}","-\frac{\sqrt{\frac{\pi }{2}} \cos (a) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{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,"Cos[a + b/x^2]/(2*b*x) - (Sqrt[Pi/2]*Cos[a]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/x])/(2*b^(3/2)) + (Sqrt[Pi/2]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/x]*Sin[a])/(2*b^(3/2))","A",5,5,12,0.4167,1,"{3409, 3385, 3354, 3352, 3351}"
124,1,8,0,0.009238,"\int \frac{\sin \left(\sqrt{x}\right)}{\sqrt{x}} \, dx","Int[Sin[Sqrt[x]]/Sqrt[x],x]","-2 \cos \left(\sqrt{x}\right)","-2 \cos \left(\sqrt{x}\right)",1,"-2*Cos[Sqrt[x]]","A",2,2,12,0.1667,1,"{3379, 2638}"
125,1,21,0,0.0204478,"\int \frac{\sin ^3\left(\sqrt{x}\right)}{\sqrt{x}} \, dx","Int[Sin[Sqrt[x]]^3/Sqrt[x],x]","\frac{2}{3} \cos ^3\left(\sqrt{x}\right)-2 \cos \left(\sqrt{x}\right)","\frac{2}{3} \cos ^3\left(\sqrt{x}\right)-2 \cos \left(\sqrt{x}\right)",1,"-2*Cos[Sqrt[x]] + (2*Cos[Sqrt[x]]^3)/3","A",3,2,14,0.1429,1,"{3379, 2633}"
126,1,22,0,0.0118392,"\int \sin \left(\sqrt{x}\right) \, dx","Int[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",3,3,6,0.5000,1,"{3361, 3296, 2637}"
127,1,69,0,0.043028,"\int \sin ^2\left(\sqrt[3]{x}\right) \, dx","Int[Sin[x^(1/3)]^2,x]","-\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)","-\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,"(-3*x^(1/3))/4 + x/2 + (3*Cos[x^(1/3)]*Sin[x^(1/3)])/4 - (3*x^(2/3)*Cos[x^(1/3)]*Sin[x^(1/3)])/2 + (3*x^(1/3)*Sin[x^(1/3)]^2)/2","A",5,5,8,0.6250,1,"{3361, 3311, 30, 2635, 8}"
128,1,87,0,0.0636996,"\int \sin ^3\left(\sqrt[3]{x}\right) \, dx","Int[Sin[x^(1/3)]^3,x]","-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)","-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,"(14*Cos[x^(1/3)])/3 - 2*x^(2/3)*Cos[x^(1/3)] - (2*Cos[x^(1/3)]^3)/9 + 4*x^(1/3)*Sin[x^(1/3)] - x^(2/3)*Cos[x^(1/3)]*Sin[x^(1/3)]^2 + (2*x^(1/3)*Sin[x^(1/3)]^3)/3","A",7,5,8,0.6250,1,"{3361, 3311, 3296, 2638, 2633}"
129,0,0,0,0.0197795,"\int (e x)^m \left(b \sin \left(c+d x^n\right)\right)^p \, dx","Int[(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,"Defer[Int][(e*x)^m*(b*Sin[c + d*x^n])^p, x]","A",0,0,0,0,-1,"{}"
130,0,0,0,0.0234132,"\int (e x)^m \left(a+b \sin \left(c+d x^n\right)\right)^p \, dx","Int[(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,"Defer[Int][(e*x)^m*(a + b*Sin[c + d*x^n])^p, x]","A",0,0,0,0,-1,"{}"
131,1,92,0,0.101912,"\int (e x)^{-1+n} \left(b \sin \left(c+d x^n\right)\right)^p \, dx","Int[(e*x)^(-1 + n)*(b*Sin[c + d*x^n])^p,x]","\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)}}","\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,"((e*x)^n*Cos[c + d*x^n]*Hypergeometric2F1[1/2, (1 + p)/2, (3 + p)/2, Sin[c + d*x^n]^2]*(b*Sin[c + d*x^n])^(1 + p))/(b*d*e*n*(1 + p)*x^n*Sqrt[Cos[c + d*x^n]^2])","A",3,3,20,0.1500,1,"{3381, 3379, 2643}"
132,0,0,0,0.0505211,"\int (e x)^{-1+2 n} \left(b \sin \left(c+d x^n\right)\right)^p \, dx","Int[(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,"((e*x)^(2*n)*Defer[Int][x^(-1 + 2*n)*(b*Sin[c + d*x^n])^p, x])/(e*x^(2*n))","A",0,0,0,0,-1,"{}"
133,1,132,0,0.1902983,"\int (e x)^{-1+n} \left(a+b \sin \left(c+d x^n\right)\right)^p \, dx","Int[(e*x)^(-1 + n)*(a + b*Sin[c + d*x^n])^p,x]","-\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}}","-\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,"-((Sqrt[2]*(e*x)^n*AppellF1[1/2, 1/2, -p, 3/2, (1 - Sin[c + d*x^n])/2, (b*(1 - Sin[c + d*x^n]))/(a + b)]*Cos[c + d*x^n]*(a + b*Sin[c + d*x^n])^p)/(d*e*n*x^n*Sqrt[1 + Sin[c + d*x^n]]*((a + b*Sin[c + d*x^n])/(a + b))^p))","A",5,5,22,0.2273,1,"{3381, 3379, 2665, 139, 138}"
134,0,0,0,0.0587778,"\int (e x)^{-1+2 n} \left(a+b \sin \left(c+d x^n\right)\right)^p \, dx","Int[(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,"((e*x)^(2*n)*Defer[Int][x^(-1 + 2*n)*(a + b*Sin[c + d*x^n])^p, x])/(e*x^(2*n))","A",0,0,0,0,-1,"{}"
135,1,25,0,0.038134,"\int \frac{\sin \left(a+b x^n\right)}{x} \, dx","Int[Sin[a + b*x^n]/x,x]","\frac{\sin (a) \text{CosIntegral}\left(b x^n\right)}{n}+\frac{\cos (a) \text{Si}\left(b x^n\right)}{n}","\frac{\sin (a) \text{CosIntegral}\left(b x^n\right)}{n}+\frac{\cos (a) \text{Si}\left(b x^n\right)}{n}",1,"(CosIntegral[b*x^n]*Sin[a])/n + (Cos[a]*SinIntegral[b*x^n])/n","A",3,3,12,0.2500,1,"{3377, 3376, 3375}"
136,1,43,0,0.0614448,"\int \frac{\sin ^2\left(a+b x^n\right)}{x} \, dx","Int[Sin[a + b*x^n]^2/x,x]","-\frac{\cos (2 a) \text{CosIntegral}\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}","-\frac{\cos (2 a) \text{CosIntegral}\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])/(2*n) + Log[x]/2 + (Sin[2*a]*SinIntegral[2*b*x^n])/(2*n)","A",5,4,14,0.2857,1,"{3425, 3378, 3376, 3375}"
137,1,67,0,0.0922735,"\int \frac{\sin ^3\left(a+b x^n\right)}{x} \, dx","Int[Sin[a + b*x^n]^3/x,x]","\frac{3 \sin (a) \text{CosIntegral}\left(b x^n\right)}{4 n}-\frac{\sin (3 a) \text{CosIntegral}\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}","\frac{3 \sin (a) \text{CosIntegral}\left(b x^n\right)}{4 n}-\frac{\sin (3 a) \text{CosIntegral}\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])/(4*n) - (CosIntegral[3*b*x^n]*Sin[3*a])/(4*n) + (3*Cos[a]*SinIntegral[b*x^n])/(4*n) - (Cos[3*a]*SinIntegral[3*b*x^n])/(4*n)","A",8,4,14,0.2857,1,"{3425, 3377, 3376, 3375}"
138,1,79,0,0.1005948,"\int \frac{\sin ^4\left(a+b x^n\right)}{x} \, dx","Int[Sin[a + b*x^n]^4/x,x]","-\frac{\cos (2 a) \text{CosIntegral}\left(2 b x^n\right)}{2 n}+\frac{\cos (4 a) \text{CosIntegral}\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}","-\frac{\cos (2 a) \text{CosIntegral}\left(2 b x^n\right)}{2 n}+\frac{\cos (4 a) \text{CosIntegral}\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,"-(Cos[2*a]*CosIntegral[2*b*x^n])/(2*n) + (Cos[4*a]*CosIntegral[4*b*x^n])/(8*n) + (3*Log[x])/8 + (Sin[2*a]*SinIntegral[2*b*x^n])/(2*n) - (Sin[4*a]*SinIntegral[4*b*x^n])/(8*n)","A",8,4,14,0.2857,1,"{3425, 3378, 3376, 3375}"
139,1,87,0,0.0270594,"\int \sin \left(a+b x^n\right) \, dx","Int[Sin[a + b*x^n],x]","\frac{i e^{i a} x \left(-i b x^n\right)^{-1/n} \text{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} \text{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} \text{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} \text{Gamma}\left(\frac{1}{n},i b x^n\right)}{2 n}",1,"((I/2)*E^(I*a)*x*Gamma[n^(-1), (-I)*b*x^n])/(n*((-I)*b*x^n)^n^(-1)) - ((I/2)*x*Gamma[n^(-1), I*b*x^n])/(E^(I*a)*n*(I*b*x^n)^n^(-1))","A",3,2,8,0.2500,1,"{3365, 2208}"
140,1,100,0,0.0721438,"\int \sin ^2\left(a+b x^n\right) \, dx","Int[Sin[a + b*x^n]^2,x]","\frac{e^{2 i a} 2^{-\frac{1}{n}-2} x \left(-i b x^n\right)^{-1/n} \text{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} \text{Gamma}\left(\frac{1}{n},2 i b x^n\right)}{n}+\frac{x}{2}","\frac{e^{2 i a} 2^{-\frac{1}{n}-2} x \left(-i b x^n\right)^{-1/n} \text{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} \text{Gamma}\left(\frac{1}{n},2 i b x^n\right)}{n}+\frac{x}{2}",1,"x/2 + (2^(-2 - n^(-1))*E^((2*I)*a)*x*Gamma[n^(-1), (-2*I)*b*x^n])/(n*((-I)*b*x^n)^n^(-1)) + (2^(-2 - n^(-1))*x*Gamma[n^(-1), (2*I)*b*x^n])/(E^((2*I)*a)*n*(I*b*x^n)^n^(-1))","A",5,3,10,0.3000,1,"{3367, 3366, 2208}"
141,1,187,0,0.0887636,"\int \sin ^3\left(a+b x^n\right) \, dx","Int[Sin[a + b*x^n]^3,x]","\frac{3 i e^{i a} x \left(-i b x^n\right)^{-1/n} \text{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} \text{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} \text{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} \text{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} \text{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} \text{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} \text{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} \text{Gamma}\left(\frac{1}{n},3 i b x^n\right)}{8 n}",1,"(((3*I)/8)*E^(I*a)*x*Gamma[n^(-1), (-I)*b*x^n])/(n*((-I)*b*x^n)^n^(-1)) - (((3*I)/8)*x*Gamma[n^(-1), I*b*x^n])/(E^(I*a)*n*(I*b*x^n)^n^(-1)) - ((I/8)*E^((3*I)*a)*x*Gamma[n^(-1), (-3*I)*b*x^n])/(3^n^(-1)*n*((-I)*b*x^n)^n^(-1)) + ((I/8)*x*Gamma[n^(-1), (3*I)*b*x^n])/(3^n^(-1)*E^((3*I)*a)*n*(I*b*x^n)^n^(-1))","A",8,3,10,0.3000,1,"{3367, 3365, 2208}"
142,1,109,0,0.0785224,"\int x^m \sin \left(a+b x^n\right) \, dx","Int[x^m*Sin[a + b*x^n],x]","\frac{i e^{i a} x^{m+1} \left(-i b x^n\right)^{-\frac{m+1}{n}} \text{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}} \text{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}} \text{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}} \text{Gamma}\left(\frac{m+1}{n},i b x^n\right)}{2 n}",1,"((I/2)*E^(I*a)*x^(1 + m)*Gamma[(1 + m)/n, (-I)*b*x^n])/(n*((-I)*b*x^n)^((1 + m)/n)) - ((I/2)*x^(1 + m)*Gamma[(1 + m)/n, I*b*x^n])/(E^(I*a)*n*(I*b*x^n)^((1 + m)/n))","A",3,2,12,0.1667,1,"{3423, 2218}"
143,1,139,0,0.1687474,"\int x^m \sin ^2\left(a+b x^n\right) \, dx","Int[x^m*Sin[a + b*x^n]^2,x]","\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}} \text{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}} \text{Gamma}\left(\frac{m+1}{n},2 i b x^n\right)}{n}+\frac{x^{m+1}}{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}} \text{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}} \text{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*(1 + m)) + (E^((2*I)*a)*x^(1 + m)*Gamma[(1 + m)/n, (-2*I)*b*x^n])/(2^((1 + m + 2*n)/n)*n*((-I)*b*x^n)^((1 + m)/n)) + (x^(1 + m)*Gamma[(1 + m)/n, (2*I)*b*x^n])/(2^((1 + m + 2*n)/n)*E^((2*I)*a)*n*(I*b*x^n)^((1 + m)/n))","A",5,3,14,0.2143,1,"{3425, 3424, 2218}"
144,1,237,0,0.2382098,"\int x^m \sin ^3\left(a+b x^n\right) \, dx","Int[x^m*Sin[a + b*x^n]^3,x]","\frac{3 i e^{i a} x^{m+1} \left(-i b x^n\right)^{-\frac{m+1}{n}} \text{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}} \text{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}} \text{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}} \text{Gamma}\left(\frac{m+1}{n},3 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}} \text{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}} \text{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}} \text{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}} \text{Gamma}\left(\frac{m+1}{n},3 i b x^n\right)}{8 n}",1,"(((3*I)/8)*E^(I*a)*x^(1 + m)*Gamma[(1 + m)/n, (-I)*b*x^n])/(n*((-I)*b*x^n)^((1 + m)/n)) - (((3*I)/8)*x^(1 + m)*Gamma[(1 + m)/n, I*b*x^n])/(E^(I*a)*n*(I*b*x^n)^((1 + m)/n)) - ((I/8)*E^((3*I)*a)*x^(1 + m)*Gamma[(1 + m)/n, (-3*I)*b*x^n])/(3^((1 + m)/n)*n*((-I)*b*x^n)^((1 + m)/n)) + ((I/8)*x^(1 + m)*Gamma[(1 + m)/n, (3*I)*b*x^n])/(3^((1 + m)/n)*E^((3*I)*a)*n*(I*b*x^n)^((1 + m)/n))","A",8,3,14,0.2143,1,"{3425, 3423, 2218}"
145,1,35,0,0.0323856,"\int x^{-1+2 n} \sin \left(a+b x^n\right) \, dx","Int[x^(-1 + 2*n)*Sin[a + b*x^n],x]","\frac{\sin \left(a+b x^n\right)}{b^2 n}-\frac{x^n \cos \left(a+b x^n\right)}{b 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,"-((x^n*Cos[a + b*x^n])/(b*n)) + Sin[a + b*x^n]/(b^2*n)","A",3,3,16,0.1875,1,"{3379, 3296, 2637}"
146,1,34,0,0.030392,"\int x^{-1+2 n} \cos \left(a+b x^n\right) \, dx","Int[x^(-1 + 2*n)*Cos[a + b*x^n],x]","\frac{\cos \left(a+b x^n\right)}{b^2 n}+\frac{x^n \sin \left(a+b x^n\right)}{b 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^2*n) + (x^n*Sin[a + b*x^n])/(b*n)","A",3,3,16,0.1875,1,"{3380, 3296, 2638}"
147,1,46,0,0.0887158,"\int x^{-1-n} \sin \left(a+b x^n\right) \, dx","Int[x^(-1 - n)*Sin[a + b*x^n],x]","\frac{b \cos (a) \text{CosIntegral}\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}","\frac{b \cos (a) \text{CosIntegral}\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*Cos[a]*CosIntegral[b*x^n])/n - Sin[a + b*x^n]/(n*x^n) - (b*Sin[a]*SinIntegral[b*x^n])/n","A",5,5,16,0.3125,1,"{3379, 3297, 3303, 3299, 3302}"
148,1,67,0,0.1202849,"\int x^{-1-n} \sin ^2\left(a+b x^n\right) \, dx","Int[x^(-1 - n)*Sin[a + b*x^n]^2,x]","\frac{b \sin (2 a) \text{CosIntegral}\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}","\frac{b \sin (2 a) \text{CosIntegral}\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/(2*n*x^n) + Cos[2*(a + b*x^n)]/(2*n*x^n) + (b*CosIntegral[2*b*x^n]*Sin[2*a])/n + (b*Cos[2*a]*SinIntegral[2*b*x^n])/n","A",7,6,18,0.3333,1,"{3425, 3380, 3297, 3303, 3299, 3302}"
149,1,113,0,0.2148157,"\int x^{-1-n} \sin ^3\left(a+b x^n\right) \, dx","Int[x^(-1 - n)*Sin[a + b*x^n]^3,x]","\frac{3 b \cos (a) \text{CosIntegral}\left(b x^n\right)}{4 n}-\frac{3 b \cos (3 a) \text{CosIntegral}\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}","\frac{3 b \cos (a) \text{CosIntegral}\left(b x^n\right)}{4 n}-\frac{3 b \cos (3 a) \text{CosIntegral}\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*Cos[a]*CosIntegral[b*x^n])/(4*n) - (3*b*Cos[3*a]*CosIntegral[3*b*x^n])/(4*n) - (3*Sin[a + b*x^n])/(4*n*x^n) + Sin[3*(a + b*x^n)]/(4*n*x^n) - (3*b*Sin[a]*SinIntegral[b*x^n])/(4*n) + (3*b*Sin[3*a]*SinIntegral[3*b*x^n])/(4*n)","A",12,6,18,0.3333,1,"{3425, 3379, 3297, 3303, 3299, 3302}"
150,1,78,0,0.1106958,"\int x^{-1-2 n} \sin \left(a+b x^n\right) \, dx","Int[x^(-1 - 2*n)*Sin[a + b*x^n],x]","-\frac{b^2 \sin (a) \text{CosIntegral}\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}","-\frac{b^2 \sin (a) \text{CosIntegral}\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,"-(b*Cos[a + b*x^n])/(2*n*x^n) - (b^2*CosIntegral[b*x^n]*Sin[a])/(2*n) - Sin[a + b*x^n]/(2*n*x^(2*n)) - (b^2*Cos[a]*SinIntegral[b*x^n])/(2*n)","A",6,5,16,0.3125,1,"{3379, 3297, 3303, 3299, 3302}"
151,1,95,0,0.1506598,"\int x^{-1-2 n} \sin ^2\left(a+b x^n\right) \, dx","Int[x^(-1 - 2*n)*Sin[a + b*x^n]^2,x]","\frac{b^2 \cos (2 a) \text{CosIntegral}\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}","\frac{b^2 \cos (2 a) \text{CosIntegral}\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/(4*n*x^(2*n)) + Cos[2*(a + b*x^n)]/(4*n*x^(2*n)) + (b^2*Cos[2*a]*CosIntegral[2*b*x^n])/n - (b*Sin[2*(a + b*x^n)])/(2*n*x^n) - (b^2*Sin[2*a]*SinIntegral[2*b*x^n])/n","A",8,6,18,0.3333,1,"{3425, 3380, 3297, 3303, 3299, 3302}"
152,1,165,0,0.2639446,"\int x^{-1-2 n} \sin ^3\left(a+b x^n\right) \, dx","Int[x^(-1 - 2*n)*Sin[a + b*x^n]^3,x]","-\frac{3 b^2 \sin (a) \text{CosIntegral}\left(b x^n\right)}{8 n}+\frac{9 b^2 \sin (3 a) \text{CosIntegral}\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}","-\frac{3 b^2 \sin (a) \text{CosIntegral}\left(b x^n\right)}{8 n}+\frac{9 b^2 \sin (3 a) \text{CosIntegral}\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*Cos[a + b*x^n])/(8*n*x^n) + (3*b*Cos[3*(a + b*x^n)])/(8*n*x^n) - (3*b^2*CosIntegral[b*x^n]*Sin[a])/(8*n) + (9*b^2*CosIntegral[3*b*x^n]*Sin[3*a])/(8*n) - (3*Sin[a + b*x^n])/(8*n*x^(2*n)) + Sin[3*(a + b*x^n)]/(8*n*x^(2*n)) - (3*b^2*Cos[a]*SinIntegral[b*x^n])/(8*n) + (9*b^2*Cos[3*a]*SinIntegral[3*b*x^n])/(8*n)","A",14,6,18,0.3333,1,"{3425, 3379, 3297, 3303, 3299, 3302}"
153,1,223,0,0.3118521,"\int (e+f x)^3 \sin \left(b (c+d x)^2\right) \, dx","Int[(e + f*x)^3*Sin[b*(c + d*x)^2],x]","\frac{3 \sqrt{\frac{\pi }{2}} f^2 (d e-c f) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} (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}","\frac{3 \sqrt{\frac{\pi }{2}} f^2 (d e-c f) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} (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,"(-3*f*(d*e - c*f)^2*Cos[b*(c + d*x)^2])/(2*b*d^4) - (3*f^2*(d*e - c*f)*(c + d*x)*Cos[b*(c + d*x)^2])/(2*b*d^4) - (f^3*(c + d*x)^2*Cos[b*(c + d*x)^2])/(2*b*d^4) + (3*f^2*(d*e - c*f)*Sqrt[Pi/2]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)])/(2*b^(3/2)*d^4) + ((d*e - c*f)^3*Sqrt[Pi/2]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)])/(Sqrt[b]*d^4) + (f^3*Sin[b*(c + d*x)^2])/(2*b^2*d^4)","A",10,8,18,0.4444,1,"{3433, 3351, 3379, 2638, 3385, 3352, 3296, 2637}"
154,1,150,0,0.1639916,"\int (e+f x)^2 \sin \left(b (c+d x)^2\right) \, dx","Int[(e + f*x)^2*Sin[b*(c + d*x)^2],x]","\frac{\sqrt{\frac{\pi }{2}} f^2 \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} (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}","\frac{\sqrt{\frac{\pi }{2}} f^2 \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} (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,"-((f*(d*e - c*f)*Cos[b*(c + d*x)^2])/(b*d^3)) - (f^2*(c + d*x)*Cos[b*(c + d*x)^2])/(2*b*d^3) + (f^2*Sqrt[Pi/2]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)])/(2*b^(3/2)*d^3) + ((d*e - c*f)^2*Sqrt[Pi/2]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)])/(Sqrt[b]*d^3)","A",7,6,18,0.3333,1,"{3433, 3351, 3379, 2638, 3385, 3352}"
155,1,69,0,0.0726357,"\int (e+f x) \sin \left(b (c+d x)^2\right) \, dx","Int[(e + f*x)*Sin[b*(c + d*x)^2],x]","\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}","\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])/(2*b*d^2) + ((d*e - c*f)*Sqrt[Pi/2]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)])/(Sqrt[b]*d^2)","A",5,4,16,0.2500,1,"{3433, 3351, 3379, 2638}"
156,1,39,0,0.0080351,"\int \sin \left(b (c+d x)^2\right) \, dx","Int[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",1,1,10,0.1000,1,"{3351}"
157,0,0,0,0.012457,"\int \frac{\sin \left(b (c+d x)^2\right)}{e+f x} \, dx","Int[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,"Defer[Int][Sin[b*(c + d*x)^2]/(e + f*x), x]","A",0,0,0,0,-1,"{}"
158,0,0,0,0.0121149,"\int \frac{\sin \left(b (c+d x)^2\right)}{(e+f x)^2} \, dx","Int[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,"Defer[Int][Sin[b*(c + d*x)^2]/(e + f*x)^2, x]","A",0,0,0,0,-1,"{}"
159,1,337,0,0.4202751,"\int (e+f x)^3 \sin \left(\frac{b}{(c+d x)^2}\right) \, dx","Int[(e + f*x)^3*Sin[b/(c + d*x)^2],x]","\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{CosIntegral}\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 \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{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}","\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{CosIntegral}\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 \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{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,"(2*b*f^2*(d*e - c*f)*(c + d*x)*Cos[b/(c + d*x)^2])/d^4 + (b*f^3*(c + d*x)^2*Cos[b/(c + d*x)^2])/(4*d^4) - (3*b*f*(d*e - c*f)^2*CosIntegral[b/(c + d*x)^2])/(2*d^4) - (Sqrt[b]*(d*e - c*f)^3*Sqrt[2*Pi]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)])/d^4 + (2*b^(3/2)*f^2*(d*e - c*f)*Sqrt[2*Pi]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)])/d^4 + ((d*e - c*f)^3*(c + d*x)*Sin[b/(c + d*x)^2])/d^4 + (3*f*(d*e - c*f)^2*(c + d*x)^2*Sin[b/(c + d*x)^2])/(2*d^4) + (f^2*(d*e - c*f)*(c + d*x)^3*Sin[b/(c + d*x)^2])/d^4 + (f^3*(c + d*x)^4*Sin[b/(c + d*x)^2])/(4*d^4) + (b^2*f^3*SinIntegral[b/(c + d*x)^2])/(4*d^4)","A",16,11,18,0.6111,1,"{3433, 3359, 3387, 3352, 3379, 3297, 3302, 3409, 3388, 3351, 3299}"
160,1,233,0,0.2492084,"\int (e+f x)^2 \sin \left(\frac{b}{(c+d x)^2}\right) \, dx","Int[(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)}{3 d^3}-\frac{b f (d e-c f) \text{CosIntegral}\left(\frac{b}{(c+d x)^2}\right)}{d^3}-\frac{\sqrt{2 \pi } \sqrt{b} (d e-c f)^2 \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{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}","\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{CosIntegral}\left(\frac{b}{(c+d x)^2}\right)}{d^3}-\frac{\sqrt{2 \pi } \sqrt{b} (d e-c f)^2 \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{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*f^2*(c + d*x)*Cos[b/(c + d*x)^2])/(3*d^3) - (b*f*(d*e - c*f)*CosIntegral[b/(c + d*x)^2])/d^3 - (Sqrt[b]*(d*e - c*f)^2*Sqrt[2*Pi]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)])/d^3 + (2*b^(3/2)*f^2*Sqrt[2*Pi]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)])/(3*d^3) + ((d*e - c*f)^2*(c + d*x)*Sin[b/(c + d*x)^2])/d^3 + (f*(d*e - c*f)*(c + d*x)^2*Sin[b/(c + d*x)^2])/d^3 + (f^2*(c + d*x)^3*Sin[b/(c + d*x)^2])/(3*d^3)","A",12,10,18,0.5556,1,"{3433, 3359, 3387, 3352, 3379, 3297, 3302, 3409, 3388, 3351}"
161,1,120,0,0.1284481,"\int (e+f x) \sin \left(\frac{b}{(c+d x)^2}\right) \, dx","Int[(e + f*x)*Sin[b/(c + d*x)^2],x]","-\frac{b f \text{CosIntegral}\left(\frac{b}{(c+d x)^2}\right)}{2 d^2}-\frac{\sqrt{2 \pi } \sqrt{b} (d e-c f) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{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}","-\frac{b f \text{CosIntegral}\left(\frac{b}{(c+d x)^2}\right)}{2 d^2}-\frac{\sqrt{2 \pi } \sqrt{b} (d e-c f) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{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,"-(b*f*CosIntegral[b/(c + d*x)^2])/(2*d^2) - (Sqrt[b]*(d*e - c*f)*Sqrt[2*Pi]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)])/d^2 + ((d*e - c*f)*(c + d*x)*Sin[b/(c + d*x)^2])/d^2 + (f*(c + d*x)^2*Sin[b/(c + d*x)^2])/(2*d^2)","A",8,7,16,0.4375,1,"{3433, 3359, 3387, 3352, 3379, 3297, 3302}"
162,1,60,0,0.0335677,"\int \sin \left(\frac{b}{(c+d x)^2}\right) \, dx","Int[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} \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{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} \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{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",3,3,10,0.3000,1,"{3359, 3387, 3352}"
163,0,0,0,0.012773,"\int \frac{\sin \left(\frac{b}{(c+d x)^2}\right)}{e+f x} \, dx","Int[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,"Defer[Int][Sin[b/(c + d*x)^2]/(e + f*x), x]","A",0,0,0,0,-1,"{}"
164,0,0,0,0.0122059,"\int \frac{\sin \left(\frac{b}{(c+d x)^2}\right)}{(e+f x)^2} \, dx","Int[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,"Defer[Int][Sin[b/(c + d*x)^2]/(e + f*x)^2, x]","A",0,0,0,0,-1,"{}"
165,1,341,0,0.5715701,"\int (e+f x)^3 \sin \left(a+b (c+d x)^2\right) \, dx","Int[(e + f*x)^3*Sin[a + b*(c + d*x)^2],x]","\frac{3 \sqrt{\frac{\pi }{2}} f^2 \cos (a) (d e-c f) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} (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 \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} (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}","\frac{3 \sqrt{\frac{\pi }{2}} f^2 \cos (a) (d e-c f) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} (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 \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} (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,"(-3*f*(d*e - c*f)^2*Cos[a + b*(c + d*x)^2])/(2*b*d^4) - (3*f^2*(d*e - c*f)*(c + d*x)*Cos[a + b*(c + d*x)^2])/(2*b*d^4) - (f^3*(c + d*x)^2*Cos[a + b*(c + d*x)^2])/(2*b*d^4) + (3*f^2*(d*e - c*f)*Sqrt[Pi/2]*Cos[a]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)])/(2*b^(3/2)*d^4) + ((d*e - c*f)^3*Sqrt[Pi/2]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)])/(Sqrt[b]*d^4) + ((d*e - c*f)^3*Sqrt[Pi/2]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)]*Sin[a])/(Sqrt[b]*d^4) - (3*f^2*(d*e - c*f)*Sqrt[Pi/2]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)]*Sin[a])/(2*b^(3/2)*d^4) + (f^3*Sin[a + b*(c + d*x)^2])/(2*b^2*d^4)","A",14,10,20,0.5000,1,"{3433, 3353, 3352, 3351, 3379, 2638, 3385, 3354, 3296, 2637}"
166,1,256,0,0.3398269,"\int (e+f x)^2 \sin \left(a+b (c+d x)^2\right) \, dx","Int[(e + f*x)^2*Sin[a + b*(c + d*x)^2],x]","\frac{\sqrt{\frac{\pi }{2}} f^2 \cos (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} (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 \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} (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}","\frac{\sqrt{\frac{\pi }{2}} f^2 \cos (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} (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 \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} (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,"-((f*(d*e - c*f)*Cos[a + b*(c + d*x)^2])/(b*d^3)) - (f^2*(c + d*x)*Cos[a + b*(c + d*x)^2])/(2*b*d^3) + (f^2*Sqrt[Pi/2]*Cos[a]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)])/(2*b^(3/2)*d^3) + ((d*e - c*f)^2*Sqrt[Pi/2]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)])/(Sqrt[b]*d^3) + ((d*e - c*f)^2*Sqrt[Pi/2]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)]*Sin[a])/(Sqrt[b]*d^3) - (f^2*Sqrt[Pi/2]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)]*Sin[a])/(2*b^(3/2)*d^3)","A",11,8,20,0.4000,1,"{3433, 3353, 3352, 3351, 3379, 2638, 3385, 3354}"
167,1,122,0,0.1777402,"\int (e+f x) \sin \left(a+b (c+d x)^2\right) \, dx","Int[(e + f*x)*Sin[a + b*(c + d*x)^2],x]","\frac{\sqrt{\frac{\pi }{2}} \sin (a) (d e-c f) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} (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}","\frac{\sqrt{\frac{\pi }{2}} \sin (a) (d e-c f) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} (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])/(2*b*d^2) + ((d*e - c*f)*Sqrt[Pi/2]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)])/(Sqrt[b]*d^2) + ((d*e - c*f)*Sqrt[Pi/2]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)]*Sin[a])/(Sqrt[b]*d^2)","A",7,6,18,0.3333,1,"{3433, 3353, 3352, 3351, 3379, 2638}"
168,1,83,0,0.0424326,"\int \sin \left(a+b (c+d x)^2\right) \, dx","Int[Sin[a + b*(c + d*x)^2],x]","\frac{\sqrt{\frac{\pi }{2}} \sin (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} (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}","\frac{\sqrt{\frac{\pi }{2}} \sin (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} (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)])/(Sqrt[b]*d) + (Sqrt[Pi/2]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)]*Sin[a])/(Sqrt[b]*d)","A",3,3,12,0.2500,1,"{3353, 3352, 3351}"
169,0,0,0,0.0126257,"\int \frac{\sin \left(a+b (c+d x)^2\right)}{e+f x} \, dx","Int[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,"Defer[Int][Sin[a + b*(c + d*x)^2]/(e + f*x), x]","A",0,0,0,0,-1,"{}"
170,0,0,0,0.0126098,"\int \frac{\sin \left(a+b (c+d x)^2\right)}{(e+f x)^2} \, dx","Int[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,"Defer[Int][Sin[a + b*(c + d*x)^2]/(e + f*x)^2, x]","A",0,0,0,0,-1,"{}"
171,1,434,0,0.4442757,"\int (e+f x)^3 \sin \left(a+b (c+d x)^3\right) \, dx","Int[(e + f*x)^3*Sin[a + b*(c + d*x)^3],x]","\frac{i e^{i a} f (c+d x)^2 (d e-c f)^2 \text{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 \text{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 \text{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 \text{Gamma}\left(\frac{1}{3},i b (c+d x)^3\right)}{6 d^4 \sqrt[3]{i b (c+d x)^3}}-\frac{e^{i a} f^3 (c+d x) \text{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) \text{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{f^2 (d e-c f) \cos \left(a+b (c+d x)^3\right)}{b d^4}-\frac{f^3 (c+d x) \cos \left(a+b (c+d x)^3\right)}{3 b d^4}","\frac{i e^{i a} f (c+d x)^2 (d e-c f)^2 \text{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 \text{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 \text{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 \text{Gamma}\left(\frac{1}{3},i b (c+d x)^3\right)}{6 d^4 \sqrt[3]{i b (c+d x)^3}}-\frac{e^{i a} f^3 (c+d x) \text{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) \text{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{f^2 (d e-c f) \cos \left(a+b (c+d x)^3\right)}{b d^4}-\frac{f^3 (c+d x) \cos \left(a+b (c+d x)^3\right)}{3 b d^4}",1,"-((f^2*(d*e - c*f)*Cos[a + b*(c + d*x)^3])/(b*d^4)) - (f^3*(c + d*x)*Cos[a + b*(c + d*x)^3])/(3*b*d^4) - (E^(I*a)*f^3*(c + d*x)*Gamma[1/3, (-I)*b*(c + d*x)^3])/(18*b*d^4*((-I)*b*(c + d*x)^3)^(1/3)) + ((I/6)*E^(I*a)*(d*e - c*f)^3*(c + d*x)*Gamma[1/3, (-I)*b*(c + d*x)^3])/(d^4*((-I)*b*(c + d*x)^3)^(1/3)) - (f^3*(c + d*x)*Gamma[1/3, I*b*(c + d*x)^3])/(18*b*d^4*E^(I*a)*(I*b*(c + d*x)^3)^(1/3)) - ((I/6)*(d*e - c*f)^3*(c + d*x)*Gamma[1/3, I*b*(c + d*x)^3])/(d^4*E^(I*a)*(I*b*(c + d*x)^3)^(1/3)) + ((I/2)*E^(I*a)*f*(d*e - c*f)^2*(c + d*x)^2*Gamma[2/3, (-I)*b*(c + d*x)^3])/(d^4*((-I)*b*(c + d*x)^3)^(2/3)) - ((I/2)*f*(d*e - c*f)^2*(c + d*x)^2*Gamma[2/3, I*b*(c + d*x)^3])/(d^4*E^(I*a)*(I*b*(c + d*x)^3)^(2/3))","A",14,9,20,0.4500,1,"{3433, 3355, 2208, 3389, 2218, 3379, 2638, 3385, 3356}"
172,1,280,0,0.276133,"\int (e+f x)^2 \sin \left(a+b (c+d x)^3\right) \, dx","Int[(e + f*x)^2*Sin[a + b*(c + d*x)^3],x]","\frac{i e^{i a} f (c+d x)^2 (d e-c f) \text{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) \text{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 \text{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 \text{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}","\frac{i e^{i a} f (c+d x)^2 (d e-c f) \text{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) \text{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 \text{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 \text{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,"-(f^2*Cos[a + b*(c + d*x)^3])/(3*b*d^3) + ((I/6)*E^(I*a)*(d*e - c*f)^2*(c + d*x)*Gamma[1/3, (-I)*b*(c + d*x)^3])/(d^3*((-I)*b*(c + d*x)^3)^(1/3)) - ((I/6)*(d*e - c*f)^2*(c + d*x)*Gamma[1/3, I*b*(c + d*x)^3])/(d^3*E^(I*a)*(I*b*(c + d*x)^3)^(1/3)) + ((I/3)*E^(I*a)*f*(d*e - c*f)*(c + d*x)^2*Gamma[2/3, (-I)*b*(c + d*x)^3])/(d^3*((-I)*b*(c + d*x)^3)^(2/3)) - ((I/3)*f*(d*e - c*f)*(c + d*x)^2*Gamma[2/3, I*b*(c + d*x)^3])/(d^3*E^(I*a)*(I*b*(c + d*x)^3)^(2/3))","A",10,7,20,0.3500,1,"{3433, 3355, 2208, 3389, 2218, 3379, 2638}"
173,1,235,0,0.1923146,"\int (e+f x) \sin \left(a+b (c+d x)^3\right) \, dx","Int[(e + f*x)*Sin[a + b*(c + d*x)^3],x]","\frac{i e^{i a} (c+d x) (d e-c f) \text{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) \text{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 \text{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 \text{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} (c+d x) (d e-c f) \text{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) \text{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 \text{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 \text{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,"((I/6)*E^(I*a)*(d*e - c*f)*(c + d*x)*Gamma[1/3, (-I)*b*(c + d*x)^3])/(d^2*((-I)*b*(c + d*x)^3)^(1/3)) - ((I/6)*(d*e - c*f)*(c + d*x)*Gamma[1/3, I*b*(c + d*x)^3])/(d^2*E^(I*a)*(I*b*(c + d*x)^3)^(1/3)) + ((I/6)*E^(I*a)*f*(c + d*x)^2*Gamma[2/3, (-I)*b*(c + d*x)^3])/(d^2*((-I)*b*(c + d*x)^3)^(2/3)) - ((I/6)*f*(c + d*x)^2*Gamma[2/3, I*b*(c + d*x)^3])/(d^2*E^(I*a)*(I*b*(c + d*x)^3)^(2/3))","A",8,5,18,0.2778,1,"{3433, 3355, 2208, 3389, 2218}"
174,1,107,0,0.028851,"\int \sin \left(a+b (c+d x)^3\right) \, dx","Int[Sin[a + b*(c + d*x)^3],x]","\frac{i e^{i a} (c+d x) \text{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) \text{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) \text{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) \text{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)*E^(I*a)*(c + d*x)*Gamma[1/3, (-I)*b*(c + d*x)^3])/(d*((-I)*b*(c + d*x)^3)^(1/3)) - ((I/6)*(c + d*x)*Gamma[1/3, I*b*(c + d*x)^3])/(d*E^(I*a)*(I*b*(c + d*x)^3)^(1/3))","A",3,2,12,0.1667,1,"{3355, 2208}"
175,0,0,0,0.012963,"\int \frac{\sin \left(a+b (c+d x)^3\right)}{e+f x} \, dx","Int[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,"Defer[Int][Sin[a + b*(c + d*x)^3]/(e + f*x), x]","A",0,0,0,0,-1,"{}"
176,0,0,0,0.0118501,"\int \frac{\sin \left(a+b (c+d x)^3\right)}{(e+f x)^2} \, dx","Int[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,"Defer[Int][Sin[a + b*(c + d*x)^3]/(e + f*x)^2, x]","A",0,0,0,0,-1,"{}"
177,1,371,0,0.4790708,"\int (e+f x)^2 \sin \left(a+\frac{b}{(c+d x)^2}\right) \, dx","Int[(e + f*x)^2*Sin[a + b/(c + d*x)^2],x]","\frac{2 \sqrt{2 \pi } b^{3/2} f^2 \sin (a) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{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{CosIntegral}\left(\frac{b}{(c+d x)^2}\right)}{d^3}-\frac{\sqrt{2 \pi } \sqrt{b} \cos (a) (d e-c f)^2 \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{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}","\frac{2 \sqrt{2 \pi } b^{3/2} f^2 \sin (a) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{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{CosIntegral}\left(\frac{b}{(c+d x)^2}\right)}{d^3}-\frac{\sqrt{2 \pi } \sqrt{b} \cos (a) (d e-c f)^2 \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{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*f^2*(c + d*x)*Cos[a + b/(c + d*x)^2])/(3*d^3) - (b*f*(d*e - c*f)*Cos[a]*CosIntegral[b/(c + d*x)^2])/d^3 - (Sqrt[b]*(d*e - c*f)^2*Sqrt[2*Pi]*Cos[a]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)])/d^3 + (2*b^(3/2)*f^2*Sqrt[2*Pi]*Cos[a]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)])/(3*d^3) + (2*b^(3/2)*f^2*Sqrt[2*Pi]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)]*Sin[a])/(3*d^3) + (Sqrt[b]*(d*e - c*f)^2*Sqrt[2*Pi]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)]*Sin[a])/d^3 + ((d*e - c*f)^2*(c + d*x)*Sin[a + b/(c + d*x)^2])/d^3 + (f*(d*e - c*f)*(c + d*x)^2*Sin[a + b/(c + d*x)^2])/d^3 + (f^2*(c + d*x)^3*Sin[a + b/(c + d*x)^2])/(3*d^3) + (b*f*(d*e - c*f)*Sin[a]*SinIntegral[b/(c + d*x)^2])/d^3","A",18,14,20,0.7000,1,"{3433, 3359, 3387, 3354, 3352, 3351, 3379, 3297, 3303, 3299, 3302, 3409, 3388, 3353}"
178,1,198,0,0.2592829,"\int (e+f x) \sin \left(a+\frac{b}{(c+d x)^2}\right) \, dx","Int[(e + f*x)*Sin[a + b/(c + d*x)^2],x]","-\frac{b f \cos (a) \text{CosIntegral}\left(\frac{b}{(c+d x)^2}\right)}{2 d^2}-\frac{\sqrt{2 \pi } \sqrt{b} \cos (a) (d e-c f) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{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}","-\frac{b f \cos (a) \text{CosIntegral}\left(\frac{b}{(c+d x)^2}\right)}{2 d^2}-\frac{\sqrt{2 \pi } \sqrt{b} \cos (a) (d e-c f) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{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*d^2) - (Sqrt[b]*(d*e - c*f)*Sqrt[2*Pi]*Cos[a]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)])/d^2 + (Sqrt[b]*(d*e - c*f)*Sqrt[2*Pi]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)]*Sin[a])/d^2 + ((d*e - c*f)*(c + d*x)*Sin[a + b/(c + d*x)^2])/d^2 + (f*(c + d*x)^2*Sin[a + b/(c + d*x)^2])/(2*d^2) + (b*f*Sin[a]*SinIntegral[b/(c + d*x)^2])/(2*d^2)","A",12,11,18,0.6111,1,"{3433, 3359, 3387, 3354, 3352, 3351, 3379, 3297, 3303, 3299, 3302}"
179,1,105,0,0.0684306,"\int \sin \left(a+\frac{b}{(c+d x)^2}\right) \, dx","Int[Sin[a + b/(c + d*x)^2],x]","-\frac{\sqrt{2 \pi } \sqrt{b} \cos (a) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{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}","-\frac{\sqrt{2 \pi } \sqrt{b} \cos (a) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{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)])/d) + (Sqrt[b]*Sqrt[2*Pi]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)]*Sin[a])/d + ((c + d*x)*Sin[a + b/(c + d*x)^2])/d","A",5,5,12,0.4167,1,"{3359, 3387, 3354, 3352, 3351}"
180,0,0,0,0.0126299,"\int \frac{\sin \left(a+\frac{b}{(c+d x)^2}\right)}{e+f x} \, dx","Int[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,"Defer[Int][Sin[a + b/(c + d*x)^2]/(e + f*x), x]","A",0,0,0,0,-1,"{}"
181,0,0,0,0.0123733,"\int \frac{\sin \left(a+\frac{b}{(c+d x)^2}\right)}{(e+f x)^2} \, dx","Int[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,"Defer[Int][Sin[a + b/(c + d*x)^2]/(e + f*x)^2, x]","A",0,0,0,0,-1,"{}"
182,1,330,0,0.3002478,"\int (e+f x)^2 \sin \left(a+\frac{b}{(c+d x)^3}\right) \, dx","Int[(e + f*x)^2*Sin[a + b/(c + d*x)^3],x]","-\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) \text{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) \text{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 \text{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 \text{Gamma}\left(-\frac{1}{3},\frac{i b}{(c+d x)^3}\right)}{6 d^3}-\frac{b f^2 \cos (a) \text{CosIntegral}\left(\frac{b}{(c+d x)^3}\right)}{3 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}","-\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) \text{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) \text{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 \text{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 \text{Gamma}\left(-\frac{1}{3},\frac{i b}{(c+d x)^3}\right)}{6 d^3}-\frac{b f^2 \cos (a) \text{CosIntegral}\left(\frac{b}{(c+d x)^3}\right)}{3 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,"-(b*f^2*Cos[a]*CosIntegral[b/(c + d*x)^3])/(3*d^3) - ((I/3)*E^(I*a)*f*(d*e - c*f)*(((-I)*b)/(c + d*x)^3)^(2/3)*(c + d*x)^2*Gamma[-2/3, ((-I)*b)/(c + d*x)^3])/d^3 + ((I/3)*f*(d*e - c*f)*((I*b)/(c + d*x)^3)^(2/3)*(c + d*x)^2*Gamma[-2/3, (I*b)/(c + d*x)^3])/(d^3*E^(I*a)) - ((I/6)*E^(I*a)*(d*e - c*f)^2*(((-I)*b)/(c + d*x)^3)^(1/3)*(c + d*x)*Gamma[-1/3, ((-I)*b)/(c + d*x)^3])/d^3 + ((I/6)*(d*e - c*f)^2*((I*b)/(c + d*x)^3)^(1/3)*(c + d*x)*Gamma[-1/3, (I*b)/(c + d*x)^3])/(d^3*E^(I*a)) + (f^2*(c + d*x)^3*Sin[a + b/(c + d*x)^3])/(3*d^3) + (b*f^2*Sin[a]*SinIntegral[b/(c + d*x)^3])/(3*d^3)","A",13,10,20,0.5000,1,"{3433, 3365, 2208, 3423, 2218, 3379, 3297, 3303, 3299, 3302}"
183,1,235,0,0.1458097,"\int (e+f x) \sin \left(a+\frac{b}{(c+d x)^3}\right) \, dx","Int[(e + f*x)*Sin[a + b/(c + d*x)^3],x]","-\frac{i e^{i a} (c+d x) \sqrt[3]{-\frac{i b}{(c+d x)^3}} (d e-c f) \text{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) \text{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} \text{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} \text{Gamma}\left(-\frac{2}{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) \text{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) \text{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} \text{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} \text{Gamma}\left(-\frac{2}{3},\frac{i b}{(c+d x)^3}\right)}{6 d^2}",1,"((-I/6)*E^(I*a)*f*(((-I)*b)/(c + d*x)^3)^(2/3)*(c + d*x)^2*Gamma[-2/3, ((-I)*b)/(c + d*x)^3])/d^2 + ((I/6)*f*((I*b)/(c + d*x)^3)^(2/3)*(c + d*x)^2*Gamma[-2/3, (I*b)/(c + d*x)^3])/(d^2*E^(I*a)) - ((I/6)*E^(I*a)*(d*e - c*f)*(((-I)*b)/(c + d*x)^3)^(1/3)*(c + d*x)*Gamma[-1/3, ((-I)*b)/(c + d*x)^3])/d^2 + ((I/6)*(d*e - c*f)*((I*b)/(c + d*x)^3)^(1/3)*(c + d*x)*Gamma[-1/3, (I*b)/(c + d*x)^3])/(d^2*E^(I*a))","A",8,5,18,0.2778,1,"{3433, 3365, 2208, 3423, 2218}"
184,1,107,0,0.0267101,"\int \sin \left(a+\frac{b}{(c+d x)^3}\right) \, dx","Int[Sin[a + b/(c + d*x)^3],x]","\frac{i e^{-i a} (c+d x) \sqrt[3]{\frac{i b}{(c+d x)^3}} \text{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}} \text{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}} \text{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}} \text{Gamma}\left(-\frac{1}{3},-\frac{i b}{(c+d x)^3}\right)}{6 d}",1,"((-I/6)*E^(I*a)*(((-I)*b)/(c + d*x)^3)^(1/3)*(c + d*x)*Gamma[-1/3, ((-I)*b)/(c + d*x)^3])/d + ((I/6)*((I*b)/(c + d*x)^3)^(1/3)*(c + d*x)*Gamma[-1/3, (I*b)/(c + d*x)^3])/(d*E^(I*a))","A",3,2,12,0.1667,1,"{3365, 2208}"
185,0,0,0,0.0132455,"\int \frac{\sin \left(a+\frac{b}{(c+d x)^3}\right)}{e+f x} \, dx","Int[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,"Defer[Int][Sin[a + b/(c + d*x)^3]/(e + f*x), x]","A",0,0,0,0,-1,"{}"
186,0,0,0,0.0134374,"\int \frac{\sin \left(a+\frac{b}{(c+d x)^3}\right)}{(e+f x)^2} \, dx","Int[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,"Defer[Int][Sin[a + b/(c + d*x)^3]/(e + f*x)^2, x]","A",0,0,0,0,-1,"{}"
187,1,410,0,0.3988396,"\int (e+f x)^2 \sin \left(a+b \sqrt{c+d x}\right) \, dx","Int[(e + f*x)^2*Sin[a + b*Sqrt[c + d*x]],x]","\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{24 f (d e-c f) \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{10 f^2 (c+d x)^2 \sin \left(a+b \sqrt{c+d x}\right)}{b^2 d^3}-\frac{120 f^2 (c+d x) \sin \left(a+b \sqrt{c+d x}\right)}{b^4 d^3}+\frac{240 f^2 \sin \left(a+b \sqrt{c+d x}\right)}{b^6 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{240 f^2 \sqrt{c+d x} \cos \left(a+b \sqrt{c+d x}\right)}{b^5 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}","\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{24 f (d e-c f) \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{10 f^2 (c+d x)^2 \sin \left(a+b \sqrt{c+d x}\right)}{b^2 d^3}-\frac{120 f^2 (c+d x) \sin \left(a+b \sqrt{c+d x}\right)}{b^4 d^3}+\frac{240 f^2 \sin \left(a+b \sqrt{c+d x}\right)}{b^6 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{240 f^2 \sqrt{c+d x} \cos \left(a+b \sqrt{c+d x}\right)}{b^5 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,"(-240*f^2*Sqrt[c + d*x]*Cos[a + b*Sqrt[c + d*x]])/(b^5*d^3) + (24*f*(d*e - c*f)*Sqrt[c + d*x]*Cos[a + b*Sqrt[c + d*x]])/(b^3*d^3) - (2*(d*e - c*f)^2*Sqrt[c + d*x]*Cos[a + b*Sqrt[c + d*x]])/(b*d^3) + (40*f^2*(c + d*x)^(3/2)*Cos[a + b*Sqrt[c + d*x]])/(b^3*d^3) - (4*f*(d*e - c*f)*(c + d*x)^(3/2)*Cos[a + b*Sqrt[c + d*x]])/(b*d^3) - (2*f^2*(c + d*x)^(5/2)*Cos[a + b*Sqrt[c + d*x]])/(b*d^3) + (240*f^2*Sin[a + b*Sqrt[c + d*x]])/(b^6*d^3) - (24*f*(d*e - c*f)*Sin[a + b*Sqrt[c + d*x]])/(b^4*d^3) + (2*(d*e - c*f)^2*Sin[a + b*Sqrt[c + d*x]])/(b^2*d^3) - (120*f^2*(c + d*x)*Sin[a + b*Sqrt[c + d*x]])/(b^4*d^3) + (12*f*(d*e - c*f)*(c + d*x)*Sin[a + b*Sqrt[c + d*x]])/(b^2*d^3) + (10*f^2*(c + d*x)^2*Sin[a + b*Sqrt[c + d*x]])/(b^2*d^3)","A",14,3,22,0.1364,1,"{3431, 3296, 2637}"
188,1,185,0,0.1592416,"\int (e+f x) \sin \left(a+b \sqrt{c+d x}\right) \, dx","Int[(e + f*x)*Sin[a + b*Sqrt[c + d*x]],x]","\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{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 \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}","\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{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 \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,"(12*f*Sqrt[c + d*x]*Cos[a + b*Sqrt[c + d*x]])/(b^3*d^2) - (2*(d*e - c*f)*Sqrt[c + d*x]*Cos[a + b*Sqrt[c + d*x]])/(b*d^2) - (2*f*(c + d*x)^(3/2)*Cos[a + b*Sqrt[c + d*x]])/(b*d^2) - (12*f*Sin[a + b*Sqrt[c + d*x]])/(b^4*d^2) + (2*(d*e - c*f)*Sin[a + b*Sqrt[c + d*x]])/(b^2*d^2) + (6*f*(c + d*x)*Sin[a + b*Sqrt[c + d*x]])/(b^2*d^2)","A",8,3,20,0.1500,1,"{3431, 3296, 2637}"
189,1,54,0,0.0277695,"\int \sin \left(a+b \sqrt{c+d x}\right) \, dx","Int[Sin[a + b*Sqrt[c + d*x]],x]","\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}","\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*Sqrt[c + d*x]*Cos[a + b*Sqrt[c + d*x]])/(b*d) + (2*Sin[a + b*Sqrt[c + d*x]])/(b^2*d)","A",3,3,14,0.2143,1,"{3361, 3296, 2637}"
190,1,238,0,0.7486636,"\int \frac{\sin \left(a+b \sqrt{c+d x}\right)}{e+f x} \, dx","Int[Sin[a + b*Sqrt[c + d*x]]/(e + f*x),x]","\frac{\sin \left(a-\frac{b \sqrt{c f-d e}}{\sqrt{f}}\right) \text{CosIntegral}\left(\frac{b \sqrt{c f-d e}}{\sqrt{f}}+b \sqrt{c+d x}\right)}{f}+\frac{\sin \left(a+\frac{b \sqrt{c f-d e}}{\sqrt{f}}\right) \text{CosIntegral}\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}","\frac{\sin \left(a-\frac{b \sqrt{c f-d e}}{\sqrt{f}}\right) \text{CosIntegral}\left(\frac{b \sqrt{c f-d e}}{\sqrt{f}}+b \sqrt{c+d x}\right)}{f}+\frac{\sin \left(a+\frac{b \sqrt{c f-d e}}{\sqrt{f}}\right) \text{CosIntegral}\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,"(CosIntegral[(b*Sqrt[-(d*e) + c*f])/Sqrt[f] + b*Sqrt[c + d*x]]*Sin[a - (b*Sqrt[-(d*e) + c*f])/Sqrt[f]])/f + (CosIntegral[(b*Sqrt[-(d*e) + c*f])/Sqrt[f] - b*Sqrt[c + d*x]]*Sin[a + (b*Sqrt[-(d*e) + c*f])/Sqrt[f]])/f - (Cos[a + (b*Sqrt[-(d*e) + c*f])/Sqrt[f]]*SinIntegral[(b*Sqrt[-(d*e) + c*f])/Sqrt[f] - b*Sqrt[c + d*x]])/f + (Cos[a - (b*Sqrt[-(d*e) + c*f])/Sqrt[f]]*SinIntegral[(b*Sqrt[-(d*e) + c*f])/Sqrt[f] + b*Sqrt[c + d*x]])/f","A",8,4,22,0.1818,1,"{3431, 3303, 3299, 3302}"
191,1,339,0,0.9826291,"\int \frac{\sin \left(a+b \sqrt{c+d x}\right)}{(e+f x)^2} \, dx","Int[Sin[a + b*Sqrt[c + d*x]]/(e + f*x)^2,x]","\frac{b d \cos \left(a+\frac{b \sqrt{c f-d e}}{\sqrt{f}}\right) \text{CosIntegral}\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{CosIntegral}\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{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)}","\frac{b d \cos \left(a+\frac{b \sqrt{c f-d e}}{\sqrt{f}}\right) \text{CosIntegral}\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{CosIntegral}\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{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,"(b*d*Cos[a + (b*Sqrt[-(d*e) + c*f])/Sqrt[f]]*CosIntegral[(b*Sqrt[-(d*e) + c*f])/Sqrt[f] - b*Sqrt[c + d*x]])/(2*f^(3/2)*Sqrt[-(d*e) + c*f]) - (b*d*Cos[a - (b*Sqrt[-(d*e) + c*f])/Sqrt[f]]*CosIntegral[(b*Sqrt[-(d*e) + c*f])/Sqrt[f] + b*Sqrt[c + d*x]])/(2*f^(3/2)*Sqrt[-(d*e) + c*f]) - Sin[a + b*Sqrt[c + d*x]]/(f*(e + f*x)) + (b*d*Sin[a + (b*Sqrt[-(d*e) + c*f])/Sqrt[f]]*SinIntegral[(b*Sqrt[-(d*e) + c*f])/Sqrt[f] - b*Sqrt[c + d*x]])/(2*f^(3/2)*Sqrt[-(d*e) + c*f]) + (b*d*Sin[a - (b*Sqrt[-(d*e) + c*f])/Sqrt[f]]*SinIntegral[(b*Sqrt[-(d*e) + c*f])/Sqrt[f] + b*Sqrt[c + d*x]])/(2*f^(3/2)*Sqrt[-(d*e) + c*f])","A",10,6,22,0.2727,1,"{3431, 3341, 3334, 3303, 3299, 3302}"
192,1,382,0,0.3055608,"\int (e+f x)^2 \sin \left(a+b (c+d x)^{3/2}\right) \, dx","Int[(e + f*x)^2*Sin[a + b*(c + d*x)^(3/2)],x]","-\frac{2 e^{i a} f \sqrt{c+d x} (d e-c f) \text{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) \text{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 \text{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 \text{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 \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 f^2 (c+d x)^{3/2} \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) \text{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) \text{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 \text{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 \text{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 \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 f^2 (c+d x)^{3/2} \cos \left(a+b (c+d x)^{3/2}\right)}{3 b d^3}",1,"(-4*f*(d*e - c*f)*Sqrt[c + d*x]*Cos[a + b*(c + d*x)^(3/2)])/(3*b*d^3) - (2*f^2*(c + d*x)^(3/2)*Cos[a + b*(c + d*x)^(3/2)])/(3*b*d^3) - (2*E^(I*a)*f*(d*e - c*f)*Sqrt[c + d*x]*Gamma[1/3, (-I)*b*(c + d*x)^(3/2)])/(9*b*d^3*((-I)*b*(c + d*x)^(3/2))^(1/3)) - (2*f*(d*e - c*f)*Sqrt[c + d*x]*Gamma[1/3, I*b*(c + d*x)^(3/2)])/(9*b*d^3*E^(I*a)*(I*b*(c + d*x)^(3/2))^(1/3)) + ((I/3)*E^(I*a)*(d*e - c*f)^2*(c + d*x)*Gamma[2/3, (-I)*b*(c + d*x)^(3/2)])/(d^3*((-I)*b*(c + d*x)^(3/2))^(2/3)) - ((I/3)*(d*e - c*f)^2*(c + d*x)*Gamma[2/3, I*b*(c + d*x)^(3/2)])/(d^3*E^(I*a)*(I*b*(c + d*x)^(3/2))^(2/3)) + (2*f^2*Sin[a + b*(c + d*x)^(3/2)])/(3*b^2*d^3)","A",12,9,22,0.4091,1,"{3433, 3389, 2218, 3385, 3356, 2208, 3379, 3296, 2637}"
193,1,291,0,0.1998996,"\int (e+f x) \sin \left(a+b (c+d x)^{3/2}\right) \, dx","Int[(e + f*x)*Sin[a + b*(c + d*x)^(3/2)],x]","\frac{i e^{i a} (c+d x) (d e-c f) \text{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) \text{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{e^{i a} f \sqrt{c+d x} \text{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} \text{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{2 f \sqrt{c+d x} \cos \left(a+b (c+d x)^{3/2}\right)}{3 b d^2}","\frac{i e^{i a} (c+d x) (d e-c f) \text{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) \text{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{e^{i a} f \sqrt{c+d x} \text{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} \text{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{2 f \sqrt{c+d x} \cos \left(a+b (c+d x)^{3/2}\right)}{3 b d^2}",1,"(-2*f*Sqrt[c + d*x]*Cos[a + b*(c + d*x)^(3/2)])/(3*b*d^2) - (E^(I*a)*f*Sqrt[c + d*x]*Gamma[1/3, (-I)*b*(c + d*x)^(3/2)])/(9*b*d^2*((-I)*b*(c + d*x)^(3/2))^(1/3)) - (f*Sqrt[c + d*x]*Gamma[1/3, I*b*(c + d*x)^(3/2)])/(9*b*d^2*E^(I*a)*(I*b*(c + d*x)^(3/2))^(1/3)) + ((I/3)*E^(I*a)*(d*e - c*f)*(c + d*x)*Gamma[2/3, (-I)*b*(c + d*x)^(3/2)])/(d^2*((-I)*b*(c + d*x)^(3/2))^(2/3)) - ((I/3)*(d*e - c*f)*(c + d*x)*Gamma[2/3, I*b*(c + d*x)^(3/2)])/(d^2*E^(I*a)*(I*b*(c + d*x)^(3/2))^(2/3))","A",9,6,20,0.3000,1,"{3433, 3389, 2218, 3385, 3356, 2208}"
194,1,115,0,0.0812329,"\int \sin \left(a+b (c+d x)^{3/2}\right) \, dx","Int[Sin[a + b*(c + d*x)^(3/2)],x]","\frac{i e^{i a} (c+d x) \text{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) \text{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) \text{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) \text{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)*E^(I*a)*(c + d*x)*Gamma[2/3, (-I)*b*(c + d*x)^(3/2)])/(d*((-I)*b*(c + d*x)^(3/2))^(2/3)) - ((I/3)*(c + d*x)*Gamma[2/3, I*b*(c + d*x)^(3/2)])/(d*E^(I*a)*(I*b*(c + d*x)^(3/2))^(2/3))","A",4,3,14,0.2143,1,"{3363, 3389, 2218}"
195,0,0,0,0.0132693,"\int \frac{\sin \left(a+b (c+d x)^{3/2}\right)}{e+f x} \, dx","Int[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,"Defer[Int][Sin[a + b*(c + d*x)^(3/2)]/(e + f*x), x]","A",0,0,0,0,-1,"{}"
196,0,0,0,0.0134022,"\int \frac{\sin \left(a+b (c+d x)^{3/2}\right)}{(e+f x)^2} \, dx","Int[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,"Defer[Int][Sin[a + b*(c + d*x)^(3/2)]/(e + f*x)^2, x]","A",0,0,0,0,-1,"{}"
197,1,611,0,0.7907975,"\int (e+f x)^2 \sin \left(a+\frac{b}{\sqrt{c+d x}}\right) \, dx","Int[(e + f*x)^2*Sin[a + b/Sqrt[c + d*x]],x]","-\frac{b^4 f \sin (a) (d e-c f) \text{CosIntegral}\left(\frac{b}{\sqrt{c+d x}}\right)}{6 d^3}+\frac{b^2 \sin (a) (d e-c f)^2 \text{CosIntegral}\left(\frac{b}{\sqrt{c+d x}}\right)}{d^3}+\frac{b^6 f^2 \sin (a) \text{CosIntegral}\left(\frac{b}{\sqrt{c+d x}}\right)}{360 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^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^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^6 f^2 \cos (a) \text{Si}\left(\frac{b}{\sqrt{c+d x}}\right)}{360 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^2 f^2 (c+d x)^2 \sin \left(a+\frac{b}{\sqrt{c+d x}}\right)}{60 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^3 f^2 (c+d x)^{3/2} \cos \left(a+\frac{b}{\sqrt{c+d x}}\right)}{180 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}","-\frac{b^4 f \sin (a) (d e-c f) \text{CosIntegral}\left(\frac{b}{\sqrt{c+d x}}\right)}{6 d^3}+\frac{b^2 \sin (a) (d e-c f)^2 \text{CosIntegral}\left(\frac{b}{\sqrt{c+d x}}\right)}{d^3}+\frac{b^6 f^2 \sin (a) \text{CosIntegral}\left(\frac{b}{\sqrt{c+d x}}\right)}{360 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^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^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^6 f^2 \cos (a) \text{Si}\left(\frac{b}{\sqrt{c+d x}}\right)}{360 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^2 f^2 (c+d x)^2 \sin \left(a+\frac{b}{\sqrt{c+d x}}\right)}{60 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^3 f^2 (c+d x)^{3/2} \cos \left(a+\frac{b}{\sqrt{c+d x}}\right)}{180 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,"(b^5*f^2*Sqrt[c + d*x]*Cos[a + b/Sqrt[c + d*x]])/(360*d^3) - (b^3*f*(d*e - c*f)*Sqrt[c + d*x]*Cos[a + b/Sqrt[c + d*x]])/(6*d^3) + (b*(d*e - c*f)^2*Sqrt[c + d*x]*Cos[a + b/Sqrt[c + d*x]])/d^3 - (b^3*f^2*(c + d*x)^(3/2)*Cos[a + b/Sqrt[c + d*x]])/(180*d^3) + (b*f*(d*e - c*f)*(c + d*x)^(3/2)*Cos[a + b/Sqrt[c + d*x]])/(3*d^3) + (b*f^2*(c + d*x)^(5/2)*Cos[a + b/Sqrt[c + d*x]])/(15*d^3) + (b^6*f^2*CosIntegral[b/Sqrt[c + d*x]]*Sin[a])/(360*d^3) - (b^4*f*(d*e - c*f)*CosIntegral[b/Sqrt[c + d*x]]*Sin[a])/(6*d^3) + (b^2*(d*e - c*f)^2*CosIntegral[b/Sqrt[c + d*x]]*Sin[a])/d^3 + (b^4*f^2*(c + d*x)*Sin[a + b/Sqrt[c + d*x]])/(360*d^3) - (b^2*f*(d*e - c*f)*(c + d*x)*Sin[a + b/Sqrt[c + d*x]])/(6*d^3) + ((d*e - c*f)^2*(c + d*x)*Sin[a + b/Sqrt[c + d*x]])/d^3 - (b^2*f^2*(c + d*x)^2*Sin[a + b/Sqrt[c + d*x]])/(60*d^3) + (f*(d*e - c*f)*(c + d*x)^2*Sin[a + b/Sqrt[c + d*x]])/d^3 + (f^2*(c + d*x)^3*Sin[a + b/Sqrt[c + d*x]])/(3*d^3) + (b^6*f^2*Cos[a]*SinIntegral[b/Sqrt[c + d*x]])/(360*d^3) - (b^4*f*(d*e - c*f)*Cos[a]*SinIntegral[b/Sqrt[c + d*x]])/(6*d^3) + (b^2*(d*e - c*f)^2*Cos[a]*SinIntegral[b/Sqrt[c + d*x]])/d^3","A",23,5,22,0.2273,1,"{3431, 3297, 3303, 3299, 3302}"
198,1,301,0,0.3933769,"\int (e+f x) \sin \left(a+\frac{b}{\sqrt{c+d x}}\right) \, dx","Int[(e + f*x)*Sin[a + b/Sqrt[c + d*x]],x]","\frac{b^2 \sin (a) (d e-c f) \text{CosIntegral}\left(\frac{b}{\sqrt{c+d x}}\right)}{d^2}-\frac{b^4 f \sin (a) \text{CosIntegral}\left(\frac{b}{\sqrt{c+d x}}\right)}{12 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^4 f \cos (a) \text{Si}\left(\frac{b}{\sqrt{c+d x}}\right)}{12 d^2}-\frac{b^2 f (c+d x) \sin \left(a+\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{(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}","\frac{b^2 \sin (a) (d e-c f) \text{CosIntegral}\left(\frac{b}{\sqrt{c+d x}}\right)}{d^2}-\frac{b^4 f \sin (a) \text{CosIntegral}\left(\frac{b}{\sqrt{c+d x}}\right)}{12 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^4 f \cos (a) \text{Si}\left(\frac{b}{\sqrt{c+d x}}\right)}{12 d^2}-\frac{b^2 f (c+d x) \sin \left(a+\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{(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,"-(b^3*f*Sqrt[c + d*x]*Cos[a + b/Sqrt[c + d*x]])/(12*d^2) + (b*(d*e - c*f)*Sqrt[c + d*x]*Cos[a + b/Sqrt[c + d*x]])/d^2 + (b*f*(c + d*x)^(3/2)*Cos[a + b/Sqrt[c + d*x]])/(6*d^2) - (b^4*f*CosIntegral[b/Sqrt[c + d*x]]*Sin[a])/(12*d^2) + (b^2*(d*e - c*f)*CosIntegral[b/Sqrt[c + d*x]]*Sin[a])/d^2 - (b^2*f*(c + d*x)*Sin[a + b/Sqrt[c + d*x]])/(12*d^2) + ((d*e - c*f)*(c + d*x)*Sin[a + b/Sqrt[c + d*x]])/d^2 + (f*(c + d*x)^2*Sin[a + b/Sqrt[c + d*x]])/(2*d^2) - (b^4*f*Cos[a]*SinIntegral[b/Sqrt[c + d*x]])/(12*d^2) + (b^2*(d*e - c*f)*Cos[a]*SinIntegral[b/Sqrt[c + d*x]])/d^2","A",14,5,20,0.2500,1,"{3431, 3297, 3303, 3299, 3302}"
199,1,94,0,0.118033,"\int \sin \left(a+\frac{b}{\sqrt{c+d x}}\right) \, dx","Int[Sin[a + b/Sqrt[c + d*x]],x]","\frac{b^2 \sin (a) \text{CosIntegral}\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}","\frac{b^2 \sin (a) \text{CosIntegral}\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]])/d + (b^2*CosIntegral[b/Sqrt[c + d*x]]*Sin[a])/d + ((c + d*x)*Sin[a + b/Sqrt[c + d*x]])/d + (b^2*Cos[a]*SinIntegral[b/Sqrt[c + d*x]])/d","A",6,5,14,0.3571,1,"{3361, 3297, 3303, 3299, 3302}"
200,1,276,0,1.2028532,"\int \frac{\sin \left(a+\frac{b}{\sqrt{c+d x}}\right)}{e+f x} \, dx","Int[Sin[a + b/Sqrt[c + d*x]]/(e + f*x),x]","\frac{\sin \left(a-\frac{b \sqrt{f}}{\sqrt{c f-d e}}\right) \text{CosIntegral}\left(\frac{b \sqrt{f}}{\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{CosIntegral}\left(\frac{b \sqrt{f}}{\sqrt{c f-d e}}-\frac{b}{\sqrt{c+d x}}\right)}{f}-\frac{2 \sin (a) \text{CosIntegral}\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}","\frac{\sin \left(a-\frac{b \sqrt{f}}{\sqrt{c f-d e}}\right) \text{CosIntegral}\left(\frac{b \sqrt{f}}{\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{CosIntegral}\left(\frac{b \sqrt{f}}{\sqrt{c f-d e}}-\frac{b}{\sqrt{c+d x}}\right)}{f}-\frac{2 \sin (a) \text{CosIntegral}\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,"(-2*CosIntegral[b/Sqrt[c + d*x]]*Sin[a])/f + (CosIntegral[(b*Sqrt[f])/Sqrt[-(d*e) + c*f] + b/Sqrt[c + d*x]]*Sin[a - (b*Sqrt[f])/Sqrt[-(d*e) + c*f]])/f + (CosIntegral[(b*Sqrt[f])/Sqrt[-(d*e) + c*f] - b/Sqrt[c + d*x]]*Sin[a + (b*Sqrt[f])/Sqrt[-(d*e) + c*f]])/f - (2*Cos[a]*SinIntegral[b/Sqrt[c + d*x]])/f - (Cos[a + (b*Sqrt[f])/Sqrt[-(d*e) + c*f]]*SinIntegral[(b*Sqrt[f])/Sqrt[-(d*e) + c*f] - b/Sqrt[c + d*x]])/f + (Cos[a - (b*Sqrt[f])/Sqrt[-(d*e) + c*f]]*SinIntegral[(b*Sqrt[f])/Sqrt[-(d*e) + c*f] + b/Sqrt[c + d*x]])/f","A",13,5,22,0.2273,1,"{3431, 3303, 3299, 3302, 3345}"
201,1,350,0,0.9290776,"\int \frac{\sin \left(a+\frac{b}{\sqrt{c+d x}}\right)}{(e+f x)^2} \, dx","Int[Sin[a + b/Sqrt[c + d*x]]/(e + f*x)^2,x]","-\frac{b d \cos \left(a+\frac{b \sqrt{f}}{\sqrt{c f-d e}}\right) \text{CosIntegral}\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{CosIntegral}\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{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)}","-\frac{b d \cos \left(a+\frac{b \sqrt{f}}{\sqrt{c f-d e}}\right) \text{CosIntegral}\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{CosIntegral}\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{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,"-(b*d*Cos[a + (b*Sqrt[f])/Sqrt[-(d*e) + c*f]]*CosIntegral[(b*Sqrt[f])/Sqrt[-(d*e) + c*f] - b/Sqrt[c + d*x]])/(2*Sqrt[f]*(-(d*e) + c*f)^(3/2)) + (b*d*Cos[a - (b*Sqrt[f])/Sqrt[-(d*e) + c*f]]*CosIntegral[(b*Sqrt[f])/Sqrt[-(d*e) + c*f] + b/Sqrt[c + d*x]])/(2*Sqrt[f]*(-(d*e) + c*f)^(3/2)) + ((c + d*x)*Sin[a + b/Sqrt[c + d*x]])/((d*e - c*f)*(e + f*x)) - (b*d*Sin[a + (b*Sqrt[f])/Sqrt[-(d*e) + c*f]]*SinIntegral[(b*Sqrt[f])/Sqrt[-(d*e) + c*f] - b/Sqrt[c + d*x]])/(2*Sqrt[f]*(-(d*e) + c*f)^(3/2)) - (b*d*Sin[a - (b*Sqrt[f])/Sqrt[-(d*e) + c*f]]*SinIntegral[(b*Sqrt[f])/Sqrt[-(d*e) + c*f] + b/Sqrt[c + d*x]])/(2*Sqrt[f]*(-(d*e) + c*f)^(3/2))","A",10,6,22,0.2727,1,"{3431, 3341, 3334, 3303, 3299, 3302}"
202,1,390,0,0.4282216,"\int (e+f x)^2 \sin \left(a+\frac{b}{(c+d x)^{3/2}}\right) \, dx","Int[(e + f*x)^2*Sin[a + b/(c + d*x)^(3/2)],x]","-\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) \text{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) \text{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 \text{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 \text{Gamma}\left(-\frac{2}{3},\frac{i b}{(c+d x)^{3/2}}\right)}{3 d^3}+\frac{b^2 f^2 \sin (a) \text{CosIntegral}\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{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}","-\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) \text{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) \text{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 \text{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 \text{Gamma}\left(-\frac{2}{3},\frac{i b}{(c+d x)^{3/2}}\right)}{3 d^3}+\frac{b^2 f^2 \sin (a) \text{CosIntegral}\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{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,"(b*f^2*(c + d*x)^(3/2)*Cos[a + b/(c + d*x)^(3/2)])/(3*d^3) - (((2*I)/3)*E^(I*a)*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)])/d^3 + (((2*I)/3)*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)])/(d^3*E^(I*a)) - ((I/3)*E^(I*a)*(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)])/d^3 + ((I/3)*(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)])/(d^3*E^(I*a)) + (b^2*f^2*CosIntegral[b/(c + d*x)^(3/2)]*Sin[a])/(3*d^3) + (f^2*(c + d*x)^3*Sin[a + b/(c + d*x)^(3/2)])/(3*d^3) + (b^2*f^2*Cos[a]*SinIntegral[b/(c + d*x)^(3/2)])/(3*d^3)","A",14,8,22,0.3636,1,"{3433, 3423, 2218, 3379, 3297, 3303, 3299, 3302}"
203,1,251,0,0.2257314,"\int (e+f x) \sin \left(a+\frac{b}{(c+d x)^{3/2}}\right) \, dx","Int[(e + f*x)*Sin[a + b/(c + d*x)^(3/2)],x]","-\frac{i e^{i a} (c+d x) \left(-\frac{i b}{(c+d x)^{3/2}}\right)^{2/3} (d e-c f) \text{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) \text{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} \text{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} \text{Gamma}\left(-\frac{4}{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) \text{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) \text{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} \text{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} \text{Gamma}\left(-\frac{4}{3},\frac{i b}{(c+d x)^{3/2}}\right)}{3 d^2}",1,"((-I/3)*E^(I*a)*f*(((-I)*b)/(c + d*x)^(3/2))^(4/3)*(c + d*x)^2*Gamma[-4/3, ((-I)*b)/(c + d*x)^(3/2)])/d^2 + ((I/3)*f*((I*b)/(c + d*x)^(3/2))^(4/3)*(c + d*x)^2*Gamma[-4/3, (I*b)/(c + d*x)^(3/2)])/(d^2*E^(I*a)) - ((I/3)*E^(I*a)*(d*e - c*f)*(((-I)*b)/(c + d*x)^(3/2))^(2/3)*(c + d*x)*Gamma[-2/3, ((-I)*b)/(c + d*x)^(3/2)])/d^2 + ((I/3)*(d*e - c*f)*((I*b)/(c + d*x)^(3/2))^(2/3)*(c + d*x)*Gamma[-2/3, (I*b)/(c + d*x)^(3/2)])/(d^2*E^(I*a))","A",8,3,20,0.1500,1,"{3433, 3423, 2218}"
204,1,115,0,0.0822319,"\int \sin \left(a+\frac{b}{(c+d x)^{3/2}}\right) \, dx","Int[Sin[a + b/(c + d*x)^(3/2)],x]","\frac{i e^{-i a} (c+d x) \left(\frac{i b}{(c+d x)^{3/2}}\right)^{2/3} \text{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} \text{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} \text{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} \text{Gamma}\left(-\frac{2}{3},-\frac{i b}{(c+d x)^{3/2}}\right)}{3 d}",1,"((-I/3)*E^(I*a)*(((-I)*b)/(c + d*x)^(3/2))^(2/3)*(c + d*x)*Gamma[-2/3, ((-I)*b)/(c + d*x)^(3/2)])/d + ((I/3)*((I*b)/(c + d*x)^(3/2))^(2/3)*(c + d*x)*Gamma[-2/3, (I*b)/(c + d*x)^(3/2)])/(d*E^(I*a))","A",4,3,14,0.2143,1,"{3363, 3423, 2218}"
205,0,0,0,0.0135741,"\int \frac{\sin \left(a+\frac{b}{(c+d x)^{3/2}}\right)}{e+f x} \, dx","Int[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,"Defer[Int][Sin[a + b/(c + d*x)^(3/2)]/(e + f*x), x]","A",0,0,0,0,-1,"{}"
206,0,0,0,0.0150614,"\int \frac{\sin \left(a+\frac{b}{(c+d x)^{3/2}}\right)}{(e+f x)^2} \, dx","Int[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,"Defer[Int][Sin[a + b/(c + d*x)^(3/2)]/(e + f*x)^2, x]","A",0,0,0,0,-1,"{}"
207,1,633,0,0.6470444,"\int (e+f x)^2 \sin \left(a+b \sqrt[3]{c+d x}\right) \, dx","Int[(e + f*x)^2*Sin[a + b*(c + d*x)^(1/3)],x]","\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{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{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{720 f (d e-c f) \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^6 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{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{6 (d e-c f)^2 \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^3 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{1008 f^2 (c+d x)^{5/3} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^4 d^3}+\frac{20160 f^2 (c+d x) \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^6 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{168 f^2 (c+d x)^2 \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^3 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{60480 f^2 (c+d x)^{2/3} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^7 d^3}-\frac{120960 f^2 \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^9 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}","\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{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{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{720 f (d e-c f) \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^6 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{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{6 (d e-c f)^2 \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^3 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{1008 f^2 (c+d x)^{5/3} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^4 d^3}+\frac{20160 f^2 (c+d x) \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^6 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{168 f^2 (c+d x)^2 \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^3 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{60480 f^2 (c+d x)^{2/3} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^7 d^3}-\frac{120960 f^2 \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^9 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,"(-120960*f^2*Cos[a + b*(c + d*x)^(1/3)])/(b^9*d^3) + (6*(d*e - c*f)^2*Cos[a + b*(c + d*x)^(1/3)])/(b^3*d^3) - (720*f*(d*e - c*f)*(c + d*x)^(1/3)*Cos[a + b*(c + d*x)^(1/3)])/(b^5*d^3) + (60480*f^2*(c + d*x)^(2/3)*Cos[a + b*(c + d*x)^(1/3)])/(b^7*d^3) - (3*(d*e - c*f)^2*(c + d*x)^(2/3)*Cos[a + b*(c + d*x)^(1/3)])/(b*d^3) + (120*f*(d*e - c*f)*(c + d*x)*Cos[a + b*(c + d*x)^(1/3)])/(b^3*d^3) - (5040*f^2*(c + d*x)^(4/3)*Cos[a + b*(c + d*x)^(1/3)])/(b^5*d^3) - (6*f*(d*e - c*f)*(c + d*x)^(5/3)*Cos[a + b*(c + d*x)^(1/3)])/(b*d^3) + (168*f^2*(c + d*x)^2*Cos[a + b*(c + d*x)^(1/3)])/(b^3*d^3) - (3*f^2*(c + d*x)^(8/3)*Cos[a + b*(c + d*x)^(1/3)])/(b*d^3) + (720*f*(d*e - c*f)*Sin[a + b*(c + d*x)^(1/3)])/(b^6*d^3) - (120960*f^2*(c + d*x)^(1/3)*Sin[a + b*(c + d*x)^(1/3)])/(b^8*d^3) + (6*(d*e - c*f)^2*(c + d*x)^(1/3)*Sin[a + b*(c + d*x)^(1/3)])/(b^2*d^3) - (360*f*(d*e - c*f)*(c + d*x)^(2/3)*Sin[a + b*(c + d*x)^(1/3)])/(b^4*d^3) + (20160*f^2*(c + d*x)*Sin[a + b*(c + d*x)^(1/3)])/(b^6*d^3) + (30*f*(d*e - c*f)*(c + d*x)^(4/3)*Sin[a + b*(c + d*x)^(1/3)])/(b^2*d^3) - (1008*f^2*(c + d*x)^(5/3)*Sin[a + b*(c + d*x)^(1/3)])/(b^4*d^3) + (24*f^2*(c + d*x)^(7/3)*Sin[a + b*(c + d*x)^(1/3)])/(b^2*d^3)","A",20,4,22,0.1818,1,"{3431, 3296, 2638, 2637}"
208,1,288,0,0.2693471,"\int (e+f x) \sin \left(a+b \sqrt[3]{c+d x}\right) \, dx","Int[(e + f*x)*Sin[a + b*(c + d*x)^(1/3)],x]","\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{6 (d e-c f) \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^3 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{180 f (c+d x)^{2/3} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^4 d^2}+\frac{360 f \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^6 d^2}+\frac{60 f (c+d x) \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^3 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{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}","\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{6 (d e-c f) \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^3 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{180 f (c+d x)^{2/3} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^4 d^2}+\frac{360 f \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^6 d^2}+\frac{60 f (c+d x) \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^3 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{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,"(6*(d*e - c*f)*Cos[a + b*(c + d*x)^(1/3)])/(b^3*d^2) - (360*f*(c + d*x)^(1/3)*Cos[a + b*(c + d*x)^(1/3)])/(b^5*d^2) - (3*(d*e - c*f)*(c + d*x)^(2/3)*Cos[a + b*(c + d*x)^(1/3)])/(b*d^2) + (60*f*(c + d*x)*Cos[a + b*(c + d*x)^(1/3)])/(b^3*d^2) - (3*f*(c + d*x)^(5/3)*Cos[a + b*(c + d*x)^(1/3)])/(b*d^2) + (360*f*Sin[a + b*(c + d*x)^(1/3)])/(b^6*d^2) + (6*(d*e - c*f)*(c + d*x)^(1/3)*Sin[a + b*(c + d*x)^(1/3)])/(b^2*d^2) - (180*f*(c + d*x)^(2/3)*Sin[a + b*(c + d*x)^(1/3)])/(b^4*d^2) + (15*f*(c + d*x)^(4/3)*Sin[a + b*(c + d*x)^(1/3)])/(b^2*d^2)","A",11,4,20,0.2000,1,"{3431, 3296, 2638, 2637}"
209,1,85,0,0.057381,"\int \sin \left(a+b \sqrt[3]{c+d x}\right) \, dx","Int[Sin[a + b*(c + d*x)^(1/3)],x]","\frac{6 \sqrt[3]{c+d x} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d}+\frac{6 \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d}-\frac{3 (c+d x)^{2/3} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b d}","\frac{6 \sqrt[3]{c+d x} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^2 d}+\frac{6 \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^3 d}-\frac{3 (c+d x)^{2/3} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b d}",1,"(6*Cos[a + b*(c + d*x)^(1/3)])/(b^3*d) - (3*(c + d*x)^(2/3)*Cos[a + b*(c + d*x)^(1/3)])/(b*d) + (6*(c + d*x)^(1/3)*Sin[a + b*(c + d*x)^(1/3)])/(b^2*d)","A",4,3,14,0.2143,1,"{3361, 3296, 2638}"
210,1,396,0,1.3898718,"\int \frac{\sin \left(a+b \sqrt[3]{c+d x}\right)}{e+f x} \, dx","Int[Sin[a + b*(c + d*x)^(1/3)]/(e + f*x),x]","\frac{\sin \left(a-\frac{b \sqrt[3]{d e-c f}}{\sqrt[3]{f}}\right) \text{CosIntegral}\left(\frac{b \sqrt[3]{d e-c f}}{\sqrt[3]{f}}+b \sqrt[3]{c+d x}\right)}{f}+\frac{\sin \left(a+\frac{\sqrt[3]{-1} b \sqrt[3]{d e-c f}}{\sqrt[3]{f}}\right) \text{CosIntegral}\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{CosIntegral}\left(\frac{(-1)^{2/3} b \sqrt[3]{d e-c f}}{\sqrt[3]{f}}+b \sqrt[3]{c+d x}\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}","\frac{\sin \left(a-\frac{b \sqrt[3]{d e-c f}}{\sqrt[3]{f}}\right) \text{CosIntegral}\left(\frac{b \sqrt[3]{d e-c f}}{\sqrt[3]{f}}+b \sqrt[3]{c+d x}\right)}{f}+\frac{\sin \left(a+\frac{\sqrt[3]{-1} b \sqrt[3]{d e-c f}}{\sqrt[3]{f}}\right) \text{CosIntegral}\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{CosIntegral}\left(\frac{(-1)^{2/3} b \sqrt[3]{d e-c f}}{\sqrt[3]{f}}+b \sqrt[3]{c+d x}\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,"(CosIntegral[(b*(d*e - c*f)^(1/3))/f^(1/3) + b*(c + d*x)^(1/3)]*Sin[a - (b*(d*e - c*f)^(1/3))/f^(1/3)])/f + (CosIntegral[((-1)^(1/3)*b*(d*e - c*f)^(1/3))/f^(1/3) - b*(c + d*x)^(1/3)]*Sin[a + ((-1)^(1/3)*b*(d*e - c*f)^(1/3))/f^(1/3)])/f + (CosIntegral[((-1)^(2/3)*b*(d*e - c*f)^(1/3))/f^(1/3) + b*(c + d*x)^(1/3)]*Sin[a - ((-1)^(2/3)*b*(d*e - c*f)^(1/3))/f^(1/3)])/f - (Cos[a + ((-1)^(1/3)*b*(d*e - c*f)^(1/3))/f^(1/3)]*SinIntegral[((-1)^(1/3)*b*(d*e - c*f)^(1/3))/f^(1/3) - b*(c + d*x)^(1/3)])/f + (Cos[a - (b*(d*e - c*f)^(1/3))/f^(1/3)]*SinIntegral[(b*(d*e - c*f)^(1/3))/f^(1/3) + b*(c + d*x)^(1/3)])/f + (Cos[a - ((-1)^(2/3)*b*(d*e - c*f)^(1/3))/f^(1/3)]*SinIntegral[((-1)^(2/3)*b*(d*e - c*f)^(1/3))/f^(1/3) + b*(c + d*x)^(1/3)])/f","A",11,4,22,0.1818,1,"{3431, 3303, 3299, 3302}"
211,1,555,0,2.1241356,"\int \frac{\sin \left(a+b \sqrt[3]{c+d x}\right)}{(e+f x)^2} \, dx","Int[Sin[a + b*(c + d*x)^(1/3)]/(e + f*x)^2,x]","-\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{CosIntegral}\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{CosIntegral}\left(\frac{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{(-1)^{2/3} b d \cos \left(a-\frac{(-1)^{2/3} b \sqrt[3]{d e-c f}}{\sqrt[3]{f}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} 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{\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)}","-\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{CosIntegral}\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{CosIntegral}\left(\frac{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{(-1)^{2/3} b d \cos \left(a-\frac{(-1)^{2/3} b \sqrt[3]{d e-c f}}{\sqrt[3]{f}}\right) \text{CosIntegral}\left(\frac{(-1)^{2/3} 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{\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,"-((-1)^(1/3)*b*d*Cos[a + ((-1)^(1/3)*b*(d*e - c*f)^(1/3))/f^(1/3)]*CosIntegral[((-1)^(1/3)*b*(d*e - c*f)^(1/3))/f^(1/3) - b*(c + d*x)^(1/3)])/(3*f^(4/3)*(d*e - c*f)^(2/3)) + (b*d*Cos[a - (b*(d*e - c*f)^(1/3))/f^(1/3)]*CosIntegral[(b*(d*e - c*f)^(1/3))/f^(1/3) + b*(c + d*x)^(1/3)])/(3*f^(4/3)*(d*e - c*f)^(2/3)) + ((-1)^(2/3)*b*d*Cos[a - ((-1)^(2/3)*b*(d*e - c*f)^(1/3))/f^(1/3)]*CosIntegral[((-1)^(2/3)*b*(d*e - c*f)^(1/3))/f^(1/3) + b*(c + d*x)^(1/3)])/(3*f^(4/3)*(d*e - c*f)^(2/3)) - Sin[a + b*(c + d*x)^(1/3)]/(f*(e + f*x)) - ((-1)^(1/3)*b*d*Sin[a + ((-1)^(1/3)*b*(d*e - c*f)^(1/3))/f^(1/3)]*SinIntegral[((-1)^(1/3)*b*(d*e - c*f)^(1/3))/f^(1/3) - b*(c + d*x)^(1/3)])/(3*f^(4/3)*(d*e - c*f)^(2/3)) - (b*d*Sin[a - (b*(d*e - c*f)^(1/3))/f^(1/3)]*SinIntegral[(b*(d*e - c*f)^(1/3))/f^(1/3) + b*(c + d*x)^(1/3)])/(3*f^(4/3)*(d*e - c*f)^(2/3)) - ((-1)^(2/3)*b*d*Sin[a - ((-1)^(2/3)*b*(d*e - c*f)^(1/3))/f^(1/3)]*SinIntegral[((-1)^(2/3)*b*(d*e - c*f)^(1/3))/f^(1/3) + b*(c + d*x)^(1/3)])/(3*f^(4/3)*(d*e - c*f)^(2/3))","A",13,6,22,0.2727,1,"{3431, 3341, 3334, 3303, 3299, 3302}"
212,1,513,0,0.5352159,"\int (e+f x)^2 \sin \left(a+b (c+d x)^{2/3}\right) \, dx","Int[(e + f*x)^2*Sin[a + b*(c + d*x)^(2/3)],x]","\frac{3 \sqrt{\frac{\pi }{2}} \cos (a) (d e-c f)^2 \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} \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{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{6 f (d e-c f) \cos \left(a+b (c+d x)^{2/3}\right)}{b^3 d^3}+\frac{315 \sqrt{\frac{\pi }{2}} f^2 \sin (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} \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{21 f^2 (c+d x)^{5/3} \sin \left(a+b (c+d x)^{2/3}\right)}{4 b^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{105 f^2 (c+d x) \cos \left(a+b (c+d x)^{2/3}\right)}{8 b^3 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}","\frac{3 \sqrt{\frac{\pi }{2}} \cos (a) (d e-c f)^2 \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} \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{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{6 f (d e-c f) \cos \left(a+b (c+d x)^{2/3}\right)}{b^3 d^3}+\frac{315 \sqrt{\frac{\pi }{2}} f^2 \sin (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} \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{21 f^2 (c+d x)^{5/3} \sin \left(a+b (c+d x)^{2/3}\right)}{4 b^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{105 f^2 (c+d x) \cos \left(a+b (c+d x)^{2/3}\right)}{8 b^3 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,"(6*f*(d*e - c*f)*Cos[a + b*(c + d*x)^(2/3)])/(b^3*d^3) - (3*(d*e - c*f)^2*(c + d*x)^(1/3)*Cos[a + b*(c + d*x)^(2/3)])/(2*b*d^3) + (105*f^2*(c + d*x)*Cos[a + b*(c + d*x)^(2/3)])/(8*b^3*d^3) - (3*f*(d*e - c*f)*(c + d*x)^(4/3)*Cos[a + b*(c + d*x)^(2/3)])/(b*d^3) - (3*f^2*(c + d*x)^(7/3)*Cos[a + b*(c + d*x)^(2/3)])/(2*b*d^3) + (3*(d*e - c*f)^2*Sqrt[Pi/2]*Cos[a]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)^(1/3)])/(2*b^(3/2)*d^3) + (315*f^2*Sqrt[Pi/2]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)^(1/3)])/(16*b^(9/2)*d^3) + (315*f^2*Sqrt[Pi/2]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)^(1/3)]*Sin[a])/(16*b^(9/2)*d^3) - (3*(d*e - c*f)^2*Sqrt[Pi/2]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)^(1/3)]*Sin[a])/(2*b^(3/2)*d^3) - (315*f^2*(c + d*x)^(1/3)*Sin[a + b*(c + d*x)^(2/3)])/(16*b^4*d^3) + (6*f*(d*e - c*f)*(c + d*x)^(2/3)*Sin[a + b*(c + d*x)^(2/3)])/(b^2*d^3) + (21*f^2*(c + d*x)^(5/3)*Sin[a + b*(c + d*x)^(2/3)])/(4*b^2*d^3)","A",17,10,22,0.4545,1,"{3433, 3385, 3354, 3352, 3351, 3379, 3296, 2638, 3386, 3353}"
213,1,243,0,0.2641733,"\int (e+f x) \sin \left(a+b (c+d x)^{2/3}\right) \, dx","Int[(e + f*x)*Sin[a + b*(c + d*x)^(2/3)],x]","\frac{3 \sqrt{\frac{\pi }{2}} \cos (a) (d e-c f) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} \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 (c+d x)^{2/3} \sin \left(a+b (c+d x)^{2/3}\right)}{b^2 d^2}+\frac{3 f \cos \left(a+b (c+d x)^{2/3}\right)}{b^3 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}","\frac{3 \sqrt{\frac{\pi }{2}} \cos (a) (d e-c f) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} \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 (c+d x)^{2/3} \sin \left(a+b (c+d x)^{2/3}\right)}{b^2 d^2}+\frac{3 f \cos \left(a+b (c+d x)^{2/3}\right)}{b^3 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*f*Cos[a + b*(c + d*x)^(2/3)])/(b^3*d^2) - (3*(d*e - c*f)*(c + d*x)^(1/3)*Cos[a + b*(c + d*x)^(2/3)])/(2*b*d^2) - (3*f*(c + d*x)^(4/3)*Cos[a + b*(c + d*x)^(2/3)])/(2*b*d^2) + (3*(d*e - c*f)*Sqrt[Pi/2]*Cos[a]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)^(1/3)])/(2*b^(3/2)*d^2) - (3*(d*e - c*f)*Sqrt[Pi/2]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)^(1/3)]*Sin[a])/(2*b^(3/2)*d^2) + (3*f*(c + d*x)^(2/3)*Sin[a + b*(c + d*x)^(2/3)])/(b^2*d^2)","A",10,8,20,0.4000,1,"{3433, 3385, 3354, 3352, 3351, 3379, 3296, 2638}"
214,1,130,0,0.0739272,"\int \sin \left(a+b (c+d x)^{2/3}\right) \, dx","Int[Sin[a + b*(c + d*x)^(2/3)],x]","\frac{3 \sqrt{\frac{\pi }{2}} \cos (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} \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}","\frac{3 \sqrt{\frac{\pi }{2}} \cos (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} \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*(c + d*x)^(1/3)*Cos[a + b*(c + d*x)^(2/3)])/(2*b*d) + (3*Sqrt[Pi/2]*Cos[a]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)^(1/3)])/(2*b^(3/2)*d) - (3*Sqrt[Pi/2]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)^(1/3)]*Sin[a])/(2*b^(3/2)*d)","A",5,5,14,0.3571,1,"{3363, 3385, 3354, 3352, 3351}"
215,0,0,0,0.0133951,"\int \frac{\sin \left(a+b (c+d x)^{2/3}\right)}{e+f x} \, dx","Int[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,"Defer[Int][Sin[a + b*(c + d*x)^(2/3)]/(e + f*x), x]","A",0,0,0,0,-1,"{}"
216,0,0,0,0.01335,"\int \frac{\sin \left(a+b (c+d x)^{2/3}\right)}{(e+f x)^2} \, dx","Int[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,"Defer[Int][Sin[a + b*(c + d*x)^(2/3)]/(e + f*x)^2, x]","A",0,0,0,0,-1,"{}"
217,1,855,0,1.0510239,"\int (e+f x)^2 \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right) \, dx","Int[(e + f*x)^2*Sin[a + b/(c + d*x)^(1/3)],x]","-\frac{f^2 \cos (a) \text{CosIntegral}\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{CosIntegral}\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{CosIntegral}\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}","-\frac{f^2 \cos (a) \text{CosIntegral}\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{CosIntegral}\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{CosIntegral}\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,"(b^5*f*(d*e - c*f)*(c + d*x)^(1/3)*Cos[a + b/(c + d*x)^(1/3)])/(120*d^3) - (b^7*f^2*(c + d*x)^(2/3)*Cos[a + b/(c + d*x)^(1/3)])/(120960*d^3) + (b*(d*e - c*f)^2*(c + d*x)^(2/3)*Cos[a + b/(c + d*x)^(1/3)])/(2*d^3) - (b^3*f*(d*e - c*f)*(c + d*x)*Cos[a + b/(c + d*x)^(1/3)])/(60*d^3) + (b^5*f^2*(c + d*x)^(4/3)*Cos[a + b/(c + d*x)^(1/3)])/(20160*d^3) + (b*f*(d*e - c*f)*(c + d*x)^(5/3)*Cos[a + b/(c + d*x)^(1/3)])/(5*d^3) - (b^3*f^2*(c + d*x)^2*Cos[a + b/(c + d*x)^(1/3)])/(1008*d^3) + (b*f^2*(c + d*x)^(8/3)*Cos[a + b/(c + d*x)^(1/3)])/(24*d^3) - (b^9*f^2*Cos[a]*CosIntegral[b/(c + d*x)^(1/3)])/(120960*d^3) + (b^3*(d*e - c*f)^2*Cos[a]*CosIntegral[b/(c + d*x)^(1/3)])/(2*d^3) + (b^6*f*(d*e - c*f)*CosIntegral[b/(c + d*x)^(1/3)]*Sin[a])/(120*d^3) + (b^8*f^2*(c + d*x)^(1/3)*Sin[a + b/(c + d*x)^(1/3)])/(120960*d^3) - (b^2*(d*e - c*f)^2*(c + d*x)^(1/3)*Sin[a + b/(c + d*x)^(1/3)])/(2*d^3) + (b^4*f*(d*e - c*f)*(c + d*x)^(2/3)*Sin[a + b/(c + d*x)^(1/3)])/(120*d^3) - (b^6*f^2*(c + d*x)*Sin[a + b/(c + d*x)^(1/3)])/(60480*d^3) + ((d*e - c*f)^2*(c + d*x)*Sin[a + b/(c + d*x)^(1/3)])/d^3 - (b^2*f*(d*e - c*f)*(c + d*x)^(4/3)*Sin[a + b/(c + d*x)^(1/3)])/(20*d^3) + (b^4*f^2*(c + d*x)^(5/3)*Sin[a + b/(c + d*x)^(1/3)])/(5040*d^3) + (f*(d*e - c*f)*(c + d*x)^2*Sin[a + b/(c + d*x)^(1/3)])/d^3 - (b^2*f^2*(c + d*x)^(7/3)*Sin[a + b/(c + d*x)^(1/3)])/(168*d^3) + (f^2*(c + d*x)^3*Sin[a + b/(c + d*x)^(1/3)])/(3*d^3) + (b^6*f*(d*e - c*f)*Cos[a]*SinIntegral[b/(c + d*x)^(1/3)])/(120*d^3) + (b^9*f^2*Sin[a]*SinIntegral[b/(c + d*x)^(1/3)])/(120960*d^3) - (b^3*(d*e - c*f)^2*Sin[a]*SinIntegral[b/(c + d*x)^(1/3)])/(2*d^3)","A",29,5,22,0.2273,1,"{3431, 3297, 3303, 3299, 3302}"
218,1,419,0,0.5040161,"\int (e+f x) \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right) \, dx","Int[(e + f*x)*Sin[a + b/(c + d*x)^(1/3)],x]","\frac{b^3 \cos (a) (d e-c f) \text{CosIntegral}\left(\frac{b}{\sqrt[3]{c+d x}}\right)}{2 d^2}+\frac{b^6 f \sin (a) \text{CosIntegral}\left(\frac{b}{\sqrt[3]{c+d x}}\right)}{240 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^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^6 f \cos (a) \text{Si}\left(\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^2 f (c+d x)^{4/3} \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{40 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^3 f (c+d x) \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{120 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}","\frac{b^3 \cos (a) (d e-c f) \text{CosIntegral}\left(\frac{b}{\sqrt[3]{c+d x}}\right)}{2 d^2}+\frac{b^6 f \sin (a) \text{CosIntegral}\left(\frac{b}{\sqrt[3]{c+d x}}\right)}{240 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^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^6 f \cos (a) \text{Si}\left(\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^2 f (c+d x)^{4/3} \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{40 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^3 f (c+d x) \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{120 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,"(b^5*f*(c + d*x)^(1/3)*Cos[a + b/(c + d*x)^(1/3)])/(240*d^2) + (b*(d*e - c*f)*(c + d*x)^(2/3)*Cos[a + b/(c + d*x)^(1/3)])/(2*d^2) - (b^3*f*(c + d*x)*Cos[a + b/(c + d*x)^(1/3)])/(120*d^2) + (b*f*(c + d*x)^(5/3)*Cos[a + b/(c + d*x)^(1/3)])/(10*d^2) + (b^3*(d*e - c*f)*Cos[a]*CosIntegral[b/(c + d*x)^(1/3)])/(2*d^2) + (b^6*f*CosIntegral[b/(c + d*x)^(1/3)]*Sin[a])/(240*d^2) - (b^2*(d*e - c*f)*(c + d*x)^(1/3)*Sin[a + b/(c + d*x)^(1/3)])/(2*d^2) + (b^4*f*(c + d*x)^(2/3)*Sin[a + b/(c + d*x)^(1/3)])/(240*d^2) + ((d*e - c*f)*(c + d*x)*Sin[a + b/(c + d*x)^(1/3)])/d^2 - (b^2*f*(c + d*x)^(4/3)*Sin[a + b/(c + d*x)^(1/3)])/(40*d^2) + (f*(c + d*x)^2*Sin[a + b/(c + d*x)^(1/3)])/(2*d^2) + (b^6*f*Cos[a]*SinIntegral[b/(c + d*x)^(1/3)])/(240*d^2) - (b^3*(d*e - c*f)*Sin[a]*SinIntegral[b/(c + d*x)^(1/3)])/(2*d^2)","A",17,5,20,0.2500,1,"{3431, 3297, 3303, 3299, 3302}"
219,1,136,0,0.1617846,"\int \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right) \, dx","Int[Sin[a + b/(c + d*x)^(1/3)],x]","\frac{b^3 \cos (a) \text{CosIntegral}\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}","\frac{b^3 \cos (a) \text{CosIntegral}\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)])/(2*d) + (b^3*Cos[a]*CosIntegral[b/(c + d*x)^(1/3)])/(2*d) - (b^2*(c + d*x)^(1/3)*Sin[a + b/(c + d*x)^(1/3)])/(2*d) + ((c + d*x)*Sin[a + b/(c + d*x)^(1/3)])/d - (b^3*Sin[a]*SinIntegral[b/(c + d*x)^(1/3)])/(2*d)","A",7,5,14,0.3571,1,"{3361, 3297, 3303, 3299, 3302}"
220,1,434,0,1.9200833,"\int \frac{\sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{e+f x} \, dx","Int[Sin[a + b/(c + d*x)^(1/3)]/(e + f*x),x]","\frac{\sin \left(a-\frac{b \sqrt[3]{f}}{\sqrt[3]{d e-c f}}\right) \text{CosIntegral}\left(\frac{b \sqrt[3]{f}}{\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{CosIntegral}\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{CosIntegral}\left(\frac{(-1)^{2/3} b \sqrt[3]{f}}{\sqrt[3]{d e-c f}}+\frac{b}{\sqrt[3]{c+d x}}\right)}{f}-\frac{3 \sin (a) \text{CosIntegral}\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}","\frac{\sin \left(a-\frac{b \sqrt[3]{f}}{\sqrt[3]{d e-c f}}\right) \text{CosIntegral}\left(\frac{b \sqrt[3]{f}}{\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{CosIntegral}\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{CosIntegral}\left(\frac{(-1)^{2/3} b \sqrt[3]{f}}{\sqrt[3]{d e-c f}}+\frac{b}{\sqrt[3]{c+d x}}\right)}{f}-\frac{3 \sin (a) \text{CosIntegral}\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,"(-3*CosIntegral[b/(c + d*x)^(1/3)]*Sin[a])/f + (CosIntegral[(b*f^(1/3))/(d*e - c*f)^(1/3) + b/(c + d*x)^(1/3)]*Sin[a - (b*f^(1/3))/(d*e - c*f)^(1/3)])/f + (CosIntegral[((-1)^(1/3)*b*f^(1/3))/(d*e - c*f)^(1/3) - b/(c + d*x)^(1/3)]*Sin[a + ((-1)^(1/3)*b*f^(1/3))/(d*e - c*f)^(1/3)])/f + (CosIntegral[((-1)^(2/3)*b*f^(1/3))/(d*e - c*f)^(1/3) + b/(c + d*x)^(1/3)]*Sin[a - ((-1)^(2/3)*b*f^(1/3))/(d*e - c*f)^(1/3)])/f - (3*Cos[a]*SinIntegral[b/(c + d*x)^(1/3)])/f - (Cos[a + ((-1)^(1/3)*b*f^(1/3))/(d*e - c*f)^(1/3)]*SinIntegral[((-1)^(1/3)*b*f^(1/3))/(d*e - c*f)^(1/3) - b/(c + d*x)^(1/3)])/f + (Cos[a - (b*f^(1/3))/(d*e - c*f)^(1/3)]*SinIntegral[(b*f^(1/3))/(d*e - c*f)^(1/3) + b/(c + d*x)^(1/3)])/f + (Cos[a - ((-1)^(2/3)*b*f^(1/3))/(d*e - c*f)^(1/3)]*SinIntegral[((-1)^(2/3)*b*f^(1/3))/(d*e - c*f)^(1/3) + b/(c + d*x)^(1/3)])/f","A",16,5,22,0.2273,1,"{3431, 3303, 3299, 3302, 3345}"
221,1,566,0,2.6298054,"\int \frac{\sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{(e+f x)^2} \, dx","Int[Sin[a + b/(c + d*x)^(1/3)]/(e + f*x)^2,x]","-\frac{b d \cos \left(a+\frac{b \sqrt[3]{f}}{\sqrt[3]{c f-d e}}\right) \text{CosIntegral}\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{CosIntegral}\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{CosIntegral}\left(\frac{\sqrt[3]{-1} 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{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)}","-\frac{b d \cos \left(a+\frac{b \sqrt[3]{f}}{\sqrt[3]{c f-d e}}\right) \text{CosIntegral}\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{CosIntegral}\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{CosIntegral}\left(\frac{\sqrt[3]{-1} 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{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,"-(b*d*Cos[a + (b*f^(1/3))/(-(d*e) + c*f)^(1/3)]*CosIntegral[(b*f^(1/3))/(-(d*e) + c*f)^(1/3) - b/(c + d*x)^(1/3)])/(3*f^(2/3)*(-(d*e) + c*f)^(4/3)) - ((-1)^(2/3)*b*d*Cos[a + ((-1)^(2/3)*b*f^(1/3))/(-(d*e) + c*f)^(1/3)]*CosIntegral[((-1)^(2/3)*b*f^(1/3))/(-(d*e) + c*f)^(1/3) - b/(c + d*x)^(1/3)])/(3*f^(2/3)*(-(d*e) + c*f)^(4/3)) + ((-1)^(1/3)*b*d*Cos[a - ((-1)^(1/3)*b*f^(1/3))/(-(d*e) + c*f)^(1/3)]*CosIntegral[((-1)^(1/3)*b*f^(1/3))/(-(d*e) + c*f)^(1/3) + b/(c + d*x)^(1/3)])/(3*f^(2/3)*(-(d*e) + c*f)^(4/3)) + ((c + d*x)*Sin[a + b/(c + d*x)^(1/3)])/((d*e - c*f)*(e + f*x)) - (b*d*Sin[a + (b*f^(1/3))/(-(d*e) + c*f)^(1/3)]*SinIntegral[(b*f^(1/3))/(-(d*e) + c*f)^(1/3) - b/(c + d*x)^(1/3)])/(3*f^(2/3)*(-(d*e) + c*f)^(4/3)) - ((-1)^(2/3)*b*d*Sin[a + ((-1)^(2/3)*b*f^(1/3))/(-(d*e) + c*f)^(1/3)]*SinIntegral[((-1)^(2/3)*b*f^(1/3))/(-(d*e) + c*f)^(1/3) - b/(c + d*x)^(1/3)])/(3*f^(2/3)*(-(d*e) + c*f)^(4/3)) - ((-1)^(1/3)*b*d*Sin[a - ((-1)^(1/3)*b*f^(1/3))/(-(d*e) + c*f)^(1/3)]*SinIntegral[((-1)^(1/3)*b*f^(1/3))/(-(d*e) + c*f)^(1/3) + b/(c + d*x)^(1/3)])/(3*f^(2/3)*(-(d*e) + c*f)^(4/3))","A",13,6,22,0.2727,1,"{3431, 3341, 3334, 3303, 3299, 3302}"
222,1,630,0,0.7476716,"\int (e+f x)^2 \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right) \, dx","Int[(e + f*x)^2*Sin[a + b/(c + d*x)^(2/3)],x]","\frac{b^3 f \cos (a) (d e-c f) \text{CosIntegral}\left(\frac{b}{(c+d x)^{2/3}}\right)}{2 d^3}+\frac{2 \sqrt{2 \pi } b^{3/2} \sin (a) (d e-c f)^2 \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{\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{b^3 f \sin (a) (d e-c f) \text{Si}\left(\frac{b}{(c+d x)^{2/3}}\right)}{2 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{16 \sqrt{2 \pi } b^{9/2} f^2 \cos (a) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{\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{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{8 b^3 f^2 (c+d x) \cos \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{315 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}","\frac{b^3 f \cos (a) (d e-c f) \text{CosIntegral}\left(\frac{b}{(c+d x)^{2/3}}\right)}{2 d^3}+\frac{2 \sqrt{2 \pi } b^{3/2} \sin (a) (d e-c f)^2 \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{\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{b^3 f \sin (a) (d e-c f) \text{Si}\left(\frac{b}{(c+d x)^{2/3}}\right)}{2 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{16 \sqrt{2 \pi } b^{9/2} f^2 \cos (a) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{\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{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{8 b^3 f^2 (c+d x) \cos \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{315 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,"(2*b*(d*e - c*f)^2*(c + d*x)^(1/3)*Cos[a + b/(c + d*x)^(2/3)])/d^3 - (8*b^3*f^2*(c + d*x)*Cos[a + b/(c + d*x)^(2/3)])/(315*d^3) + (b*f*(d*e - c*f)*(c + d*x)^(4/3)*Cos[a + b/(c + d*x)^(2/3)])/(2*d^3) + (2*b*f^2*(c + d*x)^(7/3)*Cos[a + b/(c + d*x)^(2/3)])/(21*d^3) + (b^3*f*(d*e - c*f)*Cos[a]*CosIntegral[b/(c + d*x)^(2/3)])/(2*d^3) - (16*b^(9/2)*f^2*Sqrt[2*Pi]*Cos[a]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)^(1/3)])/(315*d^3) + (2*b^(3/2)*(d*e - c*f)^2*Sqrt[2*Pi]*Cos[a]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)^(1/3)])/d^3 + (2*b^(3/2)*(d*e - c*f)^2*Sqrt[2*Pi]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)^(1/3)]*Sin[a])/d^3 + (16*b^(9/2)*f^2*Sqrt[2*Pi]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)^(1/3)]*Sin[a])/(315*d^3) + (16*b^4*f^2*(c + d*x)^(1/3)*Sin[a + b/(c + d*x)^(2/3)])/(315*d^3) - (b^2*f*(d*e - c*f)*(c + d*x)^(2/3)*Sin[a + b/(c + d*x)^(2/3)])/(2*d^3) + ((d*e - c*f)^2*(c + d*x)*Sin[a + b/(c + d*x)^(2/3)])/d^3 - (4*b^2*f^2*(c + d*x)^(5/3)*Sin[a + b/(c + d*x)^(2/3)])/(105*d^3) + (f*(d*e - c*f)*(c + d*x)^2*Sin[a + b/(c + d*x)^(2/3)])/d^3 + (f^2*(c + d*x)^3*Sin[a + b/(c + d*x)^(2/3)])/(3*d^3) - (b^3*f*(d*e - c*f)*Sin[a]*SinIntegral[b/(c + d*x)^(2/3)])/(2*d^3)","A",24,13,22,0.5909,1,"{3433, 3409, 3387, 3388, 3353, 3352, 3351, 3379, 3297, 3303, 3299, 3302, 3354}"
223,1,318,0,0.3846183,"\int (e+f x) \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right) \, dx","Int[(e + f*x)*Sin[a + b/(c + d*x)^(2/3)],x]","\frac{b^3 f \cos (a) \text{CosIntegral}\left(\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) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{\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 \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}","\frac{b^3 f \cos (a) \text{CosIntegral}\left(\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) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{\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 \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,"(2*b*(d*e - c*f)*(c + d*x)^(1/3)*Cos[a + b/(c + d*x)^(2/3)])/d^2 + (b*f*(c + d*x)^(4/3)*Cos[a + b/(c + d*x)^(2/3)])/(4*d^2) + (b^3*f*Cos[a]*CosIntegral[b/(c + d*x)^(2/3)])/(4*d^2) + (2*b^(3/2)*(d*e - c*f)*Sqrt[2*Pi]*Cos[a]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)^(1/3)])/d^2 + (2*b^(3/2)*(d*e - c*f)*Sqrt[2*Pi]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)^(1/3)]*Sin[a])/d^2 - (b^2*f*(c + d*x)^(2/3)*Sin[a + b/(c + d*x)^(2/3)])/(4*d^2) + ((d*e - c*f)*(c + d*x)*Sin[a + b/(c + d*x)^(2/3)])/d^2 + (f*(c + d*x)^2*Sin[a + b/(c + d*x)^(2/3)])/(2*d^2) - (b^3*f*Sin[a]*SinIntegral[b/(c + d*x)^(2/3)])/(4*d^2)","A",15,12,20,0.6000,1,"{3433, 3409, 3387, 3388, 3353, 3352, 3351, 3379, 3297, 3303, 3299, 3302}"
224,1,141,0,0.1118596,"\int \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right) \, dx","Int[Sin[a + b/(c + d*x)^(2/3)],x]","\frac{2 \sqrt{2 \pi } b^{3/2} \sin (a) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{\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}","\frac{2 \sqrt{2 \pi } b^{3/2} \sin (a) \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{\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)])/d + (2*b^(3/2)*Sqrt[2*Pi]*Cos[a]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)^(1/3)])/d + (2*b^(3/2)*Sqrt[2*Pi]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)^(1/3)]*Sin[a])/d + ((c + d*x)*Sin[a + b/(c + d*x)^(2/3)])/d","A",7,7,14,0.5000,1,"{3363, 3409, 3387, 3388, 3353, 3352, 3351}"
225,0,0,0,0.013414,"\int \frac{\sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{e+f x} \, dx","Int[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,"Defer[Int][Sin[a + b/(c + d*x)^(2/3)]/(e + f*x), x]","A",0,0,0,0,-1,"{}"
226,0,0,0,0.0138288,"\int \frac{\sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{(e+f x)^2} \, dx","Int[Sin[a + b/(c + d*x)^(2/3)]/(e + f*x)^2,x]","\int \frac{\sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{(e+f x)^2} \, dx","\text{Int}\left(\frac{\sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{(e+f x)^2},x\right)",0,"Defer[Int][Sin[a + b/(c + d*x)^(2/3)]/(e + f*x)^2, x]","A",0,0,0,0,-1,"{}"
227,1,289,0,0.2685176,"\int (c e+d e x)^{4/3} \sin \left(a+b \sqrt[3]{c+d x}\right) \, dx","Int[(c*e + d*e*x)^(4/3)*Sin[a + b*(c + d*x)^(1/3)],x]","\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{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{2160 e \sqrt[3]{e (c+d x)} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^6 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{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{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{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}","\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{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{2160 e \sqrt[3]{e (c+d x)} \sin \left(a+b \sqrt[3]{c+d x}\right)}{b^6 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{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{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{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,"(2160*e*(e*(c + d*x))^(1/3)*Cos[a + b*(c + d*x)^(1/3)])/(b^7*d*(c + d*x)^(1/3)) - (1080*e*(c + d*x)^(1/3)*(e*(c + d*x))^(1/3)*Cos[a + b*(c + d*x)^(1/3)])/(b^5*d) + (90*e*(c + d*x)*(e*(c + d*x))^(1/3)*Cos[a + b*(c + d*x)^(1/3)])/(b^3*d) - (3*e*(c + d*x)^(5/3)*(e*(c + d*x))^(1/3)*Cos[a + b*(c + d*x)^(1/3)])/(b*d) + (2160*e*(e*(c + d*x))^(1/3)*Sin[a + b*(c + d*x)^(1/3)])/(b^6*d) - (360*e*(c + d*x)^(2/3)*(e*(c + d*x))^(1/3)*Sin[a + b*(c + d*x)^(1/3)])/(b^4*d) + (18*e*(c + d*x)^(4/3)*(e*(c + d*x))^(1/3)*Sin[a + b*(c + d*x)^(1/3)])/(b^2*d)","A",9,4,27,0.1481,1,"{3431, 15, 3296, 2638}"
228,1,202,0,0.177942,"\int (c e+d e x)^{2/3} \sin \left(a+b \sqrt[3]{c+d x}\right) \, dx","Int[(c*e + d*e*x)^(2/3)*Sin[a + b*(c + d*x)^(1/3)],x]","\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{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{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{36 (e (c+d x))^{2/3} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^3 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}","\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{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{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{36 (e (c+d x))^{2/3} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b^3 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,"(36*(e*(c + d*x))^(2/3)*Cos[a + b*(c + d*x)^(1/3)])/(b^3*d) - (72*(e*(c + d*x))^(2/3)*Cos[a + b*(c + d*x)^(1/3)])/(b^5*d*(c + d*x)^(2/3)) - (3*(c + d*x)^(2/3)*(e*(c + d*x))^(2/3)*Cos[a + b*(c + d*x)^(1/3)])/(b*d) - (72*(e*(c + d*x))^(2/3)*Sin[a + b*(c + d*x)^(1/3)])/(b^4*d*(c + d*x)^(1/3)) + (12*(c + d*x)^(1/3)*(e*(c + d*x))^(2/3)*Sin[a + b*(c + d*x)^(1/3)])/(b^2*d)","A",7,4,27,0.1481,1,"{3431, 15, 3296, 2638}"
229,1,160,0,0.1375016,"\int \sqrt[3]{c e+d e x} \sin \left(a+b \sqrt[3]{c+d x}\right) \, dx","Int[(c*e + d*e*x)^(1/3)*Sin[a + b*(c + d*x)^(1/3)],x]","\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{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{3 (c+d x)^{2/3} \sqrt[3]{e (c+d x)} \cos \left(a+b \sqrt[3]{c+d x}\right)}{b 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{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{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,"(18*(e*(c + d*x))^(1/3)*Cos[a + b*(c + d*x)^(1/3)])/(b^3*d) - (3*(c + d*x)^(2/3)*(e*(c + d*x))^(1/3)*Cos[a + b*(c + d*x)^(1/3)])/(b*d) - (18*(e*(c + d*x))^(1/3)*Sin[a + b*(c + d*x)^(1/3)])/(b^4*d*(c + d*x)^(1/3)) + (9*(c + d*x)^(1/3)*(e*(c + d*x))^(1/3)*Sin[a + b*(c + d*x)^(1/3)])/(b^2*d)","A",6,4,27,0.1481,1,"{3431, 15, 3296, 2637}"
230,1,85,0,0.0698091,"\int \frac{\sin \left(a+b \sqrt[3]{c+d x}\right)}{\sqrt[3]{c e+d e x}} \, dx","Int[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)}{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)}}","\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*(c + d*x)^(2/3)*Cos[a + b*(c + d*x)^(1/3)])/(b*d*(e*(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",4,4,27,0.1481,1,"{3431, 15, 3296, 2637}"
231,1,42,0,0.0515908,"\int \frac{\sin \left(a+b \sqrt[3]{c+d x}\right)}{(c e+d e x)^{2/3}} \, dx","Int[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",3,3,27,0.1111,1,"{3431, 15, 2638}"
232,1,120,0,0.1461665,"\int \frac{\sin \left(a+b \sqrt[3]{c+d x}\right)}{(c e+d e x)^{4/3}} \, dx","Int[Sin[a + b*(c + d*x)^(1/3)]/(c*e + d*e*x)^(4/3),x]","\frac{3 b \cos (a) \sqrt[3]{c+d x} \text{CosIntegral}\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)}}","\frac{3 b \cos (a) \sqrt[3]{c+d x} \text{CosIntegral}\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)])/(d*e*(e*(c + d*x))^(1/3)) - (3*Sin[a + b*(c + d*x)^(1/3)])/(d*e*(e*(c + d*x))^(1/3)) - (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",6,6,27,0.2222,1,"{3431, 15, 3297, 3303, 3299, 3302}"
233,1,175,0,0.1811988,"\int \frac{\sin \left(a+b \sqrt[3]{c+d x}\right)}{(c e+d e x)^{5/3}} \, dx","Int[Sin[a + b*(c + d*x)^(1/3)]/(c*e + d*e*x)^(5/3),x]","-\frac{3 b^2 \sin (a) (c+d x)^{2/3} \text{CosIntegral}\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}}","-\frac{3 b^2 \sin (a) (c+d x)^{2/3} \text{CosIntegral}\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)])/(2*d*e*(e*(c + d*x))^(2/3)) - (3*b^2*(c + d*x)^(2/3)*CosIntegral[b*(c + d*x)^(1/3)]*Sin[a])/(2*d*e*(e*(c + d*x))^(2/3)) - (3*Sin[a + b*(c + d*x)^(1/3)])/(2*d*e*(e*(c + d*x))^(2/3)) - (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",7,6,27,0.2222,1,"{3431, 15, 3297, 3303, 3299, 3302}"
234,1,267,0,0.2626287,"\int \frac{\sin \left(a+b \sqrt[3]{c+d x}\right)}{(c e+d e x)^{7/3}} \, dx","Int[Sin[a + b*(c + d*x)^(1/3)]/(c*e + d*e*x)^(7/3),x]","\frac{b^4 \sin (a) \sqrt[3]{c+d x} \text{CosIntegral}\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^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{b^3 \cos \left(a+b \sqrt[3]{c+d x}\right)}{8 d e^2 \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)}}","\frac{b^4 \sin (a) \sqrt[3]{c+d x} \text{CosIntegral}\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^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{b^3 \cos \left(a+b \sqrt[3]{c+d x}\right)}{8 d e^2 \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*Cos[a + b*(c + d*x)^(1/3)])/(8*d*e^2*(e*(c + d*x))^(1/3)) - (b*Cos[a + b*(c + d*x)^(1/3)])/(4*d*e^2*(c + d*x)^(2/3)*(e*(c + d*x))^(1/3)) + (b^4*(c + d*x)^(1/3)*CosIntegral[b*(c + d*x)^(1/3)]*Sin[a])/(8*d*e^2*(e*(c + d*x))^(1/3)) - (3*Sin[a + b*(c + d*x)^(1/3)])/(4*d*e^2*(c + d*x)*(e*(c + d*x))^(1/3)) + (b^2*Sin[a + b*(c + d*x)^(1/3)])/(8*d*e^2*(c + d*x)^(1/3)*(e*(c + d*x))^(1/3)) + (b^4*(c + d*x)^(1/3)*Cos[a]*SinIntegral[b*(c + d*x)^(1/3)])/(8*d*e^2*(e*(c + d*x))^(1/3))","A",9,6,27,0.2222,1,"{3431, 15, 3297, 3303, 3299, 3302}"
235,1,267,0,0.2730745,"\int (c e+d e x)^{4/3} \sin \left(a+b (c+d x)^{2/3}\right) \, dx","Int[(c*e + d*e*x)^(4/3)*Sin[a + b*(c + d*x)^(2/3)],x]","-\frac{45 \sqrt{\pi } e \cos (a) \sqrt[3]{e (c+d x)} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} \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{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{45 e \sqrt[3]{e (c+d x)} \cos \left(a+b (c+d x)^{2/3}\right)}{8 b^3 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}","-\frac{45 \sqrt{\pi } e \cos (a) \sqrt[3]{e (c+d x)} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} \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{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{45 e \sqrt[3]{e (c+d x)} \cos \left(a+b (c+d x)^{2/3}\right)}{8 b^3 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,"(45*e*(e*(c + d*x))^(1/3)*Cos[a + b*(c + d*x)^(2/3)])/(8*b^3*d) - (3*e*(c + d*x)^(4/3)*(e*(c + d*x))^(1/3)*Cos[a + b*(c + d*x)^(2/3)])/(2*b*d) - (45*e*Sqrt[Pi]*(e*(c + d*x))^(1/3)*Cos[a]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)^(1/3)])/(8*Sqrt[2]*b^(7/2)*d*(c + d*x)^(1/3)) + (45*e*Sqrt[Pi]*(e*(c + d*x))^(1/3)*FresnelS[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)^(1/3)]*Sin[a])/(8*Sqrt[2]*b^(7/2)*d*(c + d*x)^(1/3)) + (15*e*(c + d*x)^(2/3)*(e*(c + d*x))^(1/3)*Sin[a + b*(c + d*x)^(2/3)])/(4*b^2*d)","A",9,8,27,0.2963,1,"{3435, 3417, 3415, 3385, 3386, 3354, 3352, 3351}"
236,1,227,0,0.1978106,"\int (c e+d e x)^{2/3} \sin \left(a+b (c+d x)^{2/3}\right) \, dx","Int[(c*e + d*e*x)^(2/3)*Sin[a + b*(c + d*x)^(2/3)],x]","-\frac{9 \sqrt{\pi } \sin (a) (e (c+d x))^{2/3} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} \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}","-\frac{9 \sqrt{\pi } \sin (a) (e (c+d x))^{2/3} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} \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*(c + d*x)^(1/3)*(e*(c + d*x))^(2/3)*Cos[a + b*(c + d*x)^(2/3)])/(2*b*d) - (9*Sqrt[Pi]*(e*(c + d*x))^(2/3)*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)^(1/3)])/(4*Sqrt[2]*b^(5/2)*d*(c + d*x)^(2/3)) - (9*Sqrt[Pi]*(e*(c + d*x))^(2/3)*FresnelC[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)^(1/3)]*Sin[a])/(4*Sqrt[2]*b^(5/2)*d*(c + d*x)^(2/3)) + (9*(e*(c + d*x))^(2/3)*Sin[a + b*(c + d*x)^(2/3)])/(4*b^2*d*(c + d*x)^(1/3))","A",8,8,27,0.2963,1,"{3435, 3417, 3415, 3385, 3386, 3353, 3352, 3351}"
237,1,89,0,0.0861527,"\int \sqrt[3]{c e+d e x} \sin \left(a+b (c+d x)^{2/3}\right) \, dx","Int[(c*e + d*e*x)^(1/3)*Sin[a + b*(c + d*x)^(2/3)],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}","\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*(c + d*x)^(1/3)*(e*(c + d*x))^(1/3)*Cos[a + b*(c + d*x)^(2/3)])/(2*b*d) + (3*(e*(c + d*x))^(1/3)*Sin[a + b*(c + d*x)^(2/3)])/(2*b^2*d*(c + d*x)^(1/3))","A",5,5,27,0.1852,1,"{3435, 3381, 3379, 3296, 2637}"
238,1,44,0,0.0628817,"\int \frac{\sin \left(a+b (c+d x)^{2/3}\right)}{\sqrt[3]{c e+d e x}} \, dx","Int[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",4,4,27,0.1481,1,"{3435, 3381, 3379, 2638}"
239,1,133,0,0.1245048,"\int \frac{\sin \left(a+b (c+d x)^{2/3}\right)}{(c e+d e x)^{2/3}} \, dx","Int[Sin[a + b*(c + d*x)^(2/3)]/(c*e + d*e*x)^(2/3),x]","\frac{3 \sqrt{\frac{\pi }{2}} \sin (a) (c+d x)^{2/3} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} \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}}","\frac{3 \sqrt{\frac{\pi }{2}} \sin (a) (c+d x)^{2/3} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} \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)])/(Sqrt[b]*d*(e*(c + d*x))^(2/3)) + (3*Sqrt[Pi/2]*(c + d*x)^(2/3)*FresnelC[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)^(1/3)]*Sin[a])/(Sqrt[b]*d*(e*(c + d*x))^(2/3))","A",6,6,27,0.2222,1,"{3435, 3417, 3383, 3353, 3352, 3351}"
240,1,168,0,0.1626496,"\int \frac{\sin \left(a+b (c+d x)^{2/3}\right)}{(c e+d e x)^{4/3}} \, dx","Int[Sin[a + b*(c + d*x)^(2/3)]/(c*e + d*e*x)^(4/3),x]","\frac{3 \sqrt{2 \pi } \sqrt{b} \cos (a) \sqrt[3]{c+d x} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} \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)}}","\frac{3 \sqrt{2 \pi } \sqrt{b} \cos (a) \sqrt[3]{c+d x} \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} \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)])/(d*e*(e*(c + d*x))^(1/3)) - (3*Sqrt[b]*Sqrt[2*Pi]*(c + d*x)^(1/3)*FresnelS[Sqrt[b]*Sqrt[2/Pi]*(c + d*x)^(1/3)]*Sin[a])/(d*e*(e*(c + d*x))^(1/3)) - (3*Sin[a + b*(c + d*x)^(2/3)])/(d*e*(e*(c + d*x))^(1/3))","A",7,7,27,0.2593,1,"{3435, 3417, 3415, 3387, 3354, 3352, 3351}"
241,1,126,0,0.1534944,"\int \frac{\sin \left(a+b (c+d x)^{2/3}\right)}{(c e+d e x)^{5/3}} \, dx","Int[Sin[a + b*(c + d*x)^(2/3)]/(c*e + d*e*x)^(5/3),x]","\frac{3 b \cos (a) (c+d x)^{2/3} \text{CosIntegral}\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}}","\frac{3 b \cos (a) (c+d x)^{2/3} \text{CosIntegral}\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)])/(2*d*e*(e*(c + d*x))^(2/3)) - (3*Sin[a + b*(c + d*x)^(2/3)])/(2*d*e*(e*(c + d*x))^(2/3)) - (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",7,7,27,0.2593,1,"{3435, 3381, 3379, 3297, 3303, 3299, 3302}"
242,1,247,0,0.2422082,"\int \sqrt[3]{c e+d e x} \sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right) \, dx","Int[(c*e + d*e*x)^(1/3)*Sin[a + b/(c + d*x)^(1/3)],x]","-\frac{b^4 \sin (a) \sqrt[3]{e (c+d x)} \text{CosIntegral}\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^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{b^3 \sqrt[3]{e (c+d x)} \cos \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}","-\frac{b^4 \sin (a) \sqrt[3]{e (c+d x)} \text{CosIntegral}\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^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{b^3 \sqrt[3]{e (c+d x)} \cos \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,"-(b^3*(e*(c + d*x))^(1/3)*Cos[a + b/(c + d*x)^(1/3)])/(8*d) + (b*(c + d*x)^(2/3)*(e*(c + d*x))^(1/3)*Cos[a + b/(c + d*x)^(1/3)])/(4*d) - (b^4*(e*(c + d*x))^(1/3)*CosIntegral[b/(c + d*x)^(1/3)]*Sin[a])/(8*d*(c + d*x)^(1/3)) - (b^2*(c + d*x)^(1/3)*(e*(c + d*x))^(1/3)*Sin[a + b/(c + d*x)^(1/3)])/(8*d) + (3*(c + d*x)*(e*(c + d*x))^(1/3)*Sin[a + b/(c + d*x)^(1/3)])/(4*d) - (b^4*(e*(c + d*x))^(1/3)*Cos[a]*SinIntegral[b/(c + d*x)^(1/3)])/(8*d*(c + d*x)^(1/3))","A",9,6,27,0.2222,1,"{3431, 15, 3297, 3303, 3299, 3302}"
243,1,168,0,0.1652012,"\int \frac{\sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{\sqrt[3]{c e+d e x}} \, dx","Int[Sin[a + b/(c + d*x)^(1/3)]/(c*e + d*e*x)^(1/3),x]","\frac{3 b^2 \sin (a) \sqrt[3]{c+d x} \text{CosIntegral}\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)}}","\frac{3 b^2 \sin (a) \sqrt[3]{c+d x} \text{CosIntegral}\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)])/(2*d*(e*(c + d*x))^(1/3)) + (3*b^2*(c + d*x)^(1/3)*CosIntegral[b/(c + d*x)^(1/3)]*Sin[a])/(2*d*(e*(c + d*x))^(1/3)) + (3*(c + d*x)*Sin[a + b/(c + d*x)^(1/3)])/(2*d*(e*(c + d*x))^(1/3)) + (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",7,6,27,0.2222,1,"{3431, 15, 3297, 3303, 3299, 3302}"
244,1,116,0,0.1291294,"\int \frac{\sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{(c e+d e x)^{2/3}} \, dx","Int[Sin[a + b/(c + d*x)^(1/3)]/(c*e + d*e*x)^(2/3),x]","-\frac{3 b \cos (a) (c+d x)^{2/3} \text{CosIntegral}\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}}","-\frac{3 b \cos (a) (c+d x)^{2/3} \text{CosIntegral}\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)])/(d*(e*(c + d*x))^(2/3)) + (3*(c + d*x)*Sin[a + b/(c + d*x)^(1/3)])/(d*(e*(c + d*x))^(2/3)) + (3*b*(c + d*x)^(2/3)*Sin[a]*SinIntegral[b/(c + d*x)^(1/3)])/(d*(e*(c + d*x))^(2/3))","A",6,6,27,0.2222,1,"{3431, 15, 3297, 3303, 3299, 3302}"
245,1,45,0,0.0474572,"\int \frac{\sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{(c e+d e x)^{4/3}} \, dx","Int[Sin[a + b/(c + d*x)^(1/3)]/(c*e + d*e*x)^(4/3),x]","\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)}}","\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)^(1/3)*Cos[a + b/(c + d*x)^(1/3)])/(b*d*e*(e*(c + d*x))^(1/3))","A",3,3,27,0.1111,1,"{3431, 15, 2638}"
246,1,91,0,0.0758568,"\int \frac{\sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{(c e+d e x)^{5/3}} \, dx","Int[Sin[a + b/(c + d*x)^(1/3)]/(c*e + d*e*x)^(5/3),x]","\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}}","\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)^(1/3)*Cos[a + b/(c + d*x)^(1/3)])/(b*d*e*(e*(c + d*x))^(2/3)) - (3*(c + d*x)^(2/3)*Sin[a + b/(c + d*x)^(1/3)])/(b^2*d*e*(e*(c + d*x))^(2/3))","A",4,4,27,0.1481,1,"{3431, 15, 3296, 2637}"
247,1,172,0,0.1478657,"\int \frac{\sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{(c e+d e x)^{7/3}} \, dx","Int[Sin[a + b/(c + d*x)^(1/3)]/(c*e + d*e*x)^(7/3),x]","\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{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{18 \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{b^3 d e^2 \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)}}","\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{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{18 \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{b^3 d e^2 \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,"(-18*Cos[a + b/(c + d*x)^(1/3)])/(b^3*d*e^2*(e*(c + d*x))^(1/3)) + (3*Cos[a + b/(c + d*x)^(1/3)])/(b*d*e^2*(c + d*x)^(2/3)*(e*(c + d*x))^(1/3)) - (9*Sin[a + b/(c + d*x)^(1/3)])/(b^2*d*e^2*(c + d*x)^(1/3)*(e*(c + d*x))^(1/3)) + (18*(c + d*x)^(1/3)*Sin[a + b/(c + d*x)^(1/3)])/(b^4*d*e^2*(e*(c + d*x))^(1/3))","A",6,4,27,0.1481,1,"{3431, 15, 3296, 2637}"
248,1,217,0,0.1886883,"\int \frac{\sin \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{(c e+d e x)^{8/3}} \, dx","Int[Sin[a + b/(c + d*x)^(1/3)]/(c*e + d*e*x)^(8/3),x]","\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{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{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{36 \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{b^3 d e^2 (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}}","\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{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{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{36 \cos \left(a+\frac{b}{\sqrt[3]{c+d x}}\right)}{b^3 d e^2 (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,"(-36*Cos[a + b/(c + d*x)^(1/3)])/(b^3*d*e^2*(e*(c + d*x))^(2/3)) + (3*Cos[a + b/(c + d*x)^(1/3)])/(b*d*e^2*(c + d*x)^(2/3)*(e*(c + d*x))^(2/3)) + (72*(c + d*x)^(2/3)*Cos[a + b/(c + d*x)^(1/3)])/(b^5*d*e^2*(e*(c + d*x))^(2/3)) - (12*Sin[a + b/(c + d*x)^(1/3)])/(b^2*d*e^2*(c + d*x)^(1/3)*(e*(c + d*x))^(2/3)) + (72*(c + d*x)^(1/3)*Sin[a + b/(c + d*x)^(1/3)])/(b^4*d*e^2*(e*(c + d*x))^(2/3))","A",7,4,27,0.1481,1,"{3431, 15, 3296, 2638}"
249,1,299,0,0.2873982,"\int (c e+d e x)^{4/3} \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right) \, dx","Int[(c*e + d*e*x)^(4/3)*Sin[a + b/(c + d*x)^(2/3)],x]","-\frac{8 \sqrt{2 \pi } b^{7/2} e \sin (a) \sqrt[3]{e (c+d x)} \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{\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{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{8 b^3 e \sqrt[3]{e (c+d x)} \cos \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}","-\frac{8 \sqrt{2 \pi } b^{7/2} e \sin (a) \sqrt[3]{e (c+d x)} \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{\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{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{8 b^3 e \sqrt[3]{e (c+d x)} \cos \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,"(-8*b^3*e*(e*(c + d*x))^(1/3)*Cos[a + b/(c + d*x)^(2/3)])/(35*d) + (6*b*e*(c + d*x)^(4/3)*(e*(c + d*x))^(1/3)*Cos[a + b/(c + d*x)^(2/3)])/(35*d) - (8*b^(7/2)*e*Sqrt[2*Pi]*(e*(c + d*x))^(1/3)*Cos[a]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)^(1/3)])/(35*d*(c + d*x)^(1/3)) - (8*b^(7/2)*e*Sqrt[2*Pi]*(e*(c + d*x))^(1/3)*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)^(1/3)]*Sin[a])/(35*d*(c + d*x)^(1/3)) - (4*b^2*e*(c + d*x)^(2/3)*(e*(c + d*x))^(1/3)*Sin[a + b/(c + d*x)^(2/3)])/(35*d) + (3*e*(c + d*x)^2*(e*(c + d*x))^(1/3)*Sin[a + b/(c + d*x)^(2/3)])/(7*d)","A",11,9,27,0.3333,1,"{3435, 3417, 3415, 3409, 3387, 3388, 3353, 3352, 3351}"
250,1,262,0,0.2275757,"\int (c e+d e x)^{2/3} \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right) \, dx","Int[(c*e + d*e*x)^(2/3)*Sin[a + b/(c + d*x)^(2/3)],x]","\frac{4 \sqrt{2} \sqrt{\pi } b^{5/2} \cos (a) (e (c+d x))^{2/3} \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{\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}","\frac{4 \sqrt{2} \sqrt{\pi } b^{5/2} \cos (a) (e (c+d x))^{2/3} \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{\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,"(2*b*(c + d*x)^(1/3)*(e*(c + d*x))^(2/3)*Cos[a + b/(c + d*x)^(2/3)])/(5*d) + (4*Sqrt[2]*b^(5/2)*Sqrt[Pi]*(e*(c + d*x))^(2/3)*Cos[a]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)^(1/3)])/(5*d*(c + d*x)^(2/3)) - (4*Sqrt[2]*b^(5/2)*Sqrt[Pi]*(e*(c + d*x))^(2/3)*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)^(1/3)]*Sin[a])/(5*d*(c + d*x)^(2/3)) - (4*b^2*(e*(c + d*x))^(2/3)*Sin[a + b/(c + d*x)^(2/3)])/(5*d*(c + d*x)^(1/3)) + (3*(c + d*x)*(e*(c + d*x))^(2/3)*Sin[a + b/(c + d*x)^(2/3)])/(5*d)","A",10,9,27,0.3333,1,"{3435, 3417, 3415, 3409, 3387, 3388, 3354, 3352, 3351}"
251,1,168,0,0.1819416,"\int \sqrt[3]{c e+d e x} \sin \left(a+\frac{b}{(c+d x)^{2/3}}\right) \, dx","Int[(c*e + d*e*x)^(1/3)*Sin[a + b/(c + d*x)^(2/3)],x]","\frac{3 b^2 \sin (a) \sqrt[3]{e (c+d x)} \text{CosIntegral}\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}","\frac{3 b^2 \sin (a) \sqrt[3]{e (c+d x)} \text{CosIntegral}\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*b*(c + d*x)^(1/3)*(e*(c + d*x))^(1/3)*Cos[a + b/(c + d*x)^(2/3)])/(4*d) + (3*b^2*(e*(c + d*x))^(1/3)*CosIntegral[b/(c + d*x)^(2/3)]*Sin[a])/(4*d*(c + d*x)^(1/3)) + (3*(c + d*x)*(e*(c + d*x))^(1/3)*Sin[a + b/(c + d*x)^(2/3)])/(4*d) + (3*b^2*(e*(c + d*x))^(1/3)*Cos[a]*SinIntegral[b/(c + d*x)^(2/3)])/(4*d*(c + d*x)^(1/3))","A",8,7,27,0.2593,1,"{3435, 3381, 3379, 3297, 3303, 3299, 3302}"
252,1,122,0,0.145402,"\int \frac{\sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{\sqrt[3]{c e+d e x}} \, dx","Int[Sin[a + b/(c + d*x)^(2/3)]/(c*e + d*e*x)^(1/3),x]","-\frac{3 b \cos (a) \sqrt[3]{c+d x} \text{CosIntegral}\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)}}","-\frac{3 b \cos (a) \sqrt[3]{c+d x} \text{CosIntegral}\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)])/(2*d*(e*(c + d*x))^(1/3)) + (3*(c + d*x)*Sin[a + b/(c + d*x)^(2/3)])/(2*d*(e*(c + d*x))^(1/3)) + (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",7,7,27,0.2593,1,"{3435, 3381, 3379, 3297, 3303, 3299, 3302}"
253,1,164,0,0.1576294,"\int \frac{\sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{(c e+d e x)^{2/3}} \, dx","Int[Sin[a + b/(c + d*x)^(2/3)]/(c*e + d*e*x)^(2/3),x]","-\frac{3 \sqrt{2 \pi } \sqrt{b} \cos (a) (c+d x)^{2/3} \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{\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}}","-\frac{3 \sqrt{2 \pi } \sqrt{b} \cos (a) (c+d x)^{2/3} \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{\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)])/(d*(e*(c + d*x))^(2/3)) + (3*Sqrt[b]*Sqrt[2*Pi]*(c + d*x)^(2/3)*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)^(1/3)]*Sin[a])/(d*(e*(c + d*x))^(2/3)) + (3*(c + d*x)*Sin[a + b/(c + d*x)^(2/3)])/(d*(e*(c + d*x))^(2/3))","A",8,8,27,0.2963,1,"{3435, 3417, 3415, 3359, 3387, 3354, 3352, 3351}"
254,1,141,0,0.1377528,"\int \frac{\sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{(c e+d e x)^{4/3}} \, dx","Int[Sin[a + b/(c + d*x)^(2/3)]/(c*e + d*e*x)^(4/3),x]","-\frac{3 \sqrt{\pi } \sin (a) \sqrt[3]{c+d x} \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{\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)}}","-\frac{3 \sqrt{\pi } \sin (a) \sqrt[3]{c+d x} \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{\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]*(c + d*x)^(1/3)*Cos[a]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)^(1/3)])/(Sqrt[2]*Sqrt[b]*d*e*(e*(c + d*x))^(1/3)) - (3*Sqrt[Pi]*(c + d*x)^(1/3)*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)^(1/3)]*Sin[a])/(Sqrt[2]*Sqrt[b]*d*e*(e*(c + d*x))^(1/3))","A",6,6,27,0.2222,1,"{3435, 3417, 3383, 3353, 3352, 3351}"
255,1,47,0,0.066342,"\int \frac{\sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{(c e+d e x)^{5/3}} \, dx","Int[Sin[a + b/(c + d*x)^(2/3)]/(c*e + d*e*x)^(5/3),x]","\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}}","\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)^(2/3)*Cos[a + b/(c + d*x)^(2/3)])/(2*b*d*e*(e*(c + d*x))^(2/3))","A",4,4,27,0.1481,1,"{3435, 3381, 3379, 2638}"
256,1,95,0,0.0955332,"\int \frac{\sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{(c e+d e x)^{7/3}} \, dx","Int[Sin[a + b/(c + d*x)^(2/3)]/(c*e + d*e*x)^(7/3),x]","\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)}}","\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*Cos[a + b/(c + d*x)^(2/3)])/(2*b*d*e^2*(c + d*x)^(1/3)*(e*(c + d*x))^(1/3)) - (3*(c + d*x)^(1/3)*Sin[a + b/(c + d*x)^(2/3)])/(2*b^2*d*e^2*(e*(c + d*x))^(1/3))","A",5,5,27,0.1852,1,"{3435, 3381, 3379, 3296, 2637}"
257,1,237,0,0.2451372,"\int \frac{\sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{(c e+d e x)^{8/3}} \, dx","Int[Sin[a + b/(c + d*x)^(2/3)]/(c*e + d*e*x)^(8/3),x]","\frac{9 \sqrt{\frac{\pi }{2}} \sin (a) (c+d x)^{2/3} \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{\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}}","\frac{9 \sqrt{\frac{\pi }{2}} \sin (a) (c+d x)^{2/3} \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{\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,"(3*Cos[a + b/(c + d*x)^(2/3)])/(2*b*d*e^2*(c + d*x)^(1/3)*(e*(c + d*x))^(2/3)) + (9*Sqrt[Pi/2]*(c + d*x)^(2/3)*Cos[a]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)^(1/3)])/(4*b^(5/2)*d*e^2*(e*(c + d*x))^(2/3)) + (9*Sqrt[Pi/2]*(c + d*x)^(2/3)*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)^(1/3)]*Sin[a])/(4*b^(5/2)*d*e^2*(e*(c + d*x))^(2/3)) - (9*(c + d*x)^(1/3)*Sin[a + b/(c + d*x)^(2/3)])/(4*b^2*d*e^2*(e*(c + d*x))^(2/3))","A",9,9,27,0.3333,1,"{3435, 3417, 3415, 3409, 3385, 3386, 3353, 3352, 3351}"
258,1,277,0,0.2646569,"\int \frac{\sin \left(a+\frac{b}{(c+d x)^{2/3}}\right)}{(c e+d e x)^{10/3}} \, dx","Int[Sin[a + b/(c + d*x)^(2/3)]/(c*e + d*e*x)^(10/3),x]","\frac{45 \sqrt{\pi } \cos (a) \sqrt[3]{c+d x} \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{\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{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{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{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)}}","\frac{45 \sqrt{\pi } \cos (a) \sqrt[3]{c+d x} \text{FresnelC}\left(\frac{\sqrt{\frac{2}{\pi }} \sqrt{b}}{\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{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{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{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,"(-45*Cos[a + b/(c + d*x)^(2/3)])/(8*b^3*d*e^3*(e*(c + d*x))^(1/3)) + (3*Cos[a + b/(c + d*x)^(2/3)])/(2*b*d*e^3*(c + d*x)^(4/3)*(e*(c + d*x))^(1/3)) + (45*Sqrt[Pi]*(c + d*x)^(1/3)*Cos[a]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)^(1/3)])/(8*Sqrt[2]*b^(7/2)*d*e^3*(e*(c + d*x))^(1/3)) - (45*Sqrt[Pi]*(c + d*x)^(1/3)*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/(c + d*x)^(1/3)]*Sin[a])/(8*Sqrt[2]*b^(7/2)*d*e^3*(e*(c + d*x))^(1/3)) - (15*Sin[a + b/(c + d*x)^(2/3)])/(4*b^2*d*e^3*(c + d*x)^(2/3)*(e*(c + d*x))^(1/3))","A",10,9,27,0.3333,1,"{3435, 3417, 3415, 3409, 3385, 3386, 3354, 3352, 3351}"
259,0,0,0,0.009114,"\int (e x)^m \sin \left(a+b (c+d x)^n\right) \, dx","Int[(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,"Defer[Int][(e*x)^m*Sin[a + b*(c + d*x)^n], x]","A",0,0,0,0,-1,"{}"
260,1,503,0,0.3914093,"\int x^3 \sin \left(a+b (c+d x)^n\right) \, dx","Int[x^3*Sin[a + b*(c + d*x)^n],x]","\frac{3 i e^{i a} c^2 (c+d x)^2 \left(-i b (c+d x)^n\right)^{-2/n} \text{Gamma}\left(\frac{2}{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} \text{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} \text{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} \text{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} \text{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} \text{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} \text{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} \text{Gamma}\left(\frac{4}{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} \text{Gamma}\left(\frac{2}{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} \text{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} \text{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} \text{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} \text{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} \text{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} \text{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} \text{Gamma}\left(\frac{4}{n},i b (c+d x)^n\right)}{2 d^4 n}",1,"((-I/2)*c^3*E^(I*a)*(c + d*x)*Gamma[n^(-1), (-I)*b*(c + d*x)^n])/(d^4*n*((-I)*b*(c + d*x)^n)^n^(-1)) + ((I/2)*c^3*(c + d*x)*Gamma[n^(-1), I*b*(c + d*x)^n])/(d^4*E^(I*a)*n*(I*b*(c + d*x)^n)^n^(-1)) + (((3*I)/2)*c^2*E^(I*a)*(c + d*x)^2*Gamma[2/n, (-I)*b*(c + d*x)^n])/(d^4*n*((-I)*b*(c + d*x)^n)^(2/n)) - (((3*I)/2)*c^2*(c + d*x)^2*Gamma[2/n, I*b*(c + d*x)^n])/(d^4*E^(I*a)*n*(I*b*(c + d*x)^n)^(2/n)) - (((3*I)/2)*c*E^(I*a)*(c + d*x)^3*Gamma[3/n, (-I)*b*(c + d*x)^n])/(d^4*n*((-I)*b*(c + d*x)^n)^(3/n)) + (((3*I)/2)*c*(c + d*x)^3*Gamma[3/n, I*b*(c + d*x)^n])/(d^4*E^(I*a)*n*(I*b*(c + d*x)^n)^(3/n)) + ((I/2)*E^(I*a)*(c + d*x)^4*Gamma[4/n, (-I)*b*(c + d*x)^n])/(d^4*n*((-I)*b*(c + d*x)^n)^(4/n)) - ((I/2)*(c + d*x)^4*Gamma[4/n, I*b*(c + d*x)^n])/(d^4*E^(I*a)*n*(I*b*(c + d*x)^n)^(4/n))","A",14,5,16,0.3125,1,"{3433, 3365, 2208, 3423, 2218}"
261,1,369,0,0.2494247,"\int x^2 \sin \left(a+b (c+d x)^n\right) \, dx","Int[x^2*Sin[a + b*(c + d*x)^n],x]","\frac{i e^{i a} c^2 (c+d x) \left(-i b (c+d x)^n\right)^{-1/n} \text{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} \text{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} \text{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} \text{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} \text{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} \text{Gamma}\left(\frac{3}{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} \text{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} \text{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} \text{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} \text{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} \text{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} \text{Gamma}\left(\frac{3}{n},i b (c+d x)^n\right)}{2 d^3 n}",1,"((I/2)*c^2*E^(I*a)*(c + d*x)*Gamma[n^(-1), (-I)*b*(c + d*x)^n])/(d^3*n*((-I)*b*(c + d*x)^n)^n^(-1)) - ((I/2)*c^2*(c + d*x)*Gamma[n^(-1), I*b*(c + d*x)^n])/(d^3*E^(I*a)*n*(I*b*(c + d*x)^n)^n^(-1)) - (I*c*E^(I*a)*(c + d*x)^2*Gamma[2/n, (-I)*b*(c + d*x)^n])/(d^3*n*((-I)*b*(c + d*x)^n)^(2/n)) + (I*c*(c + d*x)^2*Gamma[2/n, I*b*(c + d*x)^n])/(d^3*E^(I*a)*n*(I*b*(c + d*x)^n)^(2/n)) + ((I/2)*E^(I*a)*(c + d*x)^3*Gamma[3/n, (-I)*b*(c + d*x)^n])/(d^3*n*((-I)*b*(c + d*x)^n)^(3/n)) - ((I/2)*(c + d*x)^3*Gamma[3/n, I*b*(c + d*x)^n])/(d^3*E^(I*a)*n*(I*b*(c + d*x)^n)^(3/n))","A",11,5,16,0.3125,1,"{3433, 3365, 2208, 3423, 2218}"
262,1,243,0,0.1314539,"\int x \sin \left(a+b (c+d x)^n\right) \, dx","Int[x*Sin[a + b*(c + d*x)^n],x]","\frac{i e^{i a} (c+d x)^2 \left(-i b (c+d x)^n\right)^{-2/n} \text{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} \text{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} \text{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} \text{Gamma}\left(\frac{2}{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} \text{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} \text{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} \text{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} \text{Gamma}\left(\frac{2}{n},i b (c+d x)^n\right)}{2 d^2 n}",1,"((-I/2)*c*E^(I*a)*(c + d*x)*Gamma[n^(-1), (-I)*b*(c + d*x)^n])/(d^2*n*((-I)*b*(c + d*x)^n)^n^(-1)) + ((I/2)*c*(c + d*x)*Gamma[n^(-1), I*b*(c + d*x)^n])/(d^2*E^(I*a)*n*(I*b*(c + d*x)^n)^n^(-1)) + ((I/2)*E^(I*a)*(c + d*x)^2*Gamma[2/n, (-I)*b*(c + d*x)^n])/(d^2*n*((-I)*b*(c + d*x)^n)^(2/n)) - ((I/2)*(c + d*x)^2*Gamma[2/n, I*b*(c + d*x)^n])/(d^2*E^(I*a)*n*(I*b*(c + d*x)^n)^(2/n))","A",8,5,14,0.3571,1,"{3433, 3365, 2208, 3423, 2218}"
263,1,117,0,0.0293592,"\int \sin \left(a+b (c+d x)^n\right) \, dx","Int[Sin[a + b*(c + d*x)^n],x]","\frac{i e^{i a} (c+d x) \left(-i b (c+d x)^n\right)^{-1/n} \text{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} \text{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} \text{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} \text{Gamma}\left(\frac{1}{n},i b (c+d x)^n\right)}{2 d n}",1,"((I/2)*E^(I*a)*(c + d*x)*Gamma[n^(-1), (-I)*b*(c + d*x)^n])/(d*n*((-I)*b*(c + d*x)^n)^n^(-1)) - ((I/2)*(c + d*x)*Gamma[n^(-1), I*b*(c + d*x)^n])/(d*E^(I*a)*n*(I*b*(c + d*x)^n)^n^(-1))","A",3,2,12,0.1667,1,"{3365, 2208}"
264,0,0,0,0.0092419,"\int \frac{\sin \left(a+b (c+d x)^n\right)}{x} \, dx","Int[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,"Defer[Int][Sin[a + b*(c + d*x)^n]/x, x]","A",0,0,0,0,-1,"{}"
265,0,0,0,0.009085,"\int \frac{\sin \left(a+b (c+d x)^n\right)}{x^2} \, dx","Int[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,"Defer[Int][Sin[a + b*(c + d*x)^n]/x^2, x]","A",0,0,0,0,-1,"{}"
266,1,519,0,0.5341268,"\int x^3 \left(a+b \sin \left(c+d (f+g x)^n\right)\right) \, dx","Int[x^3*(a + b*Sin[c + d*(f + g*x)^n]),x]","\frac{3 i b e^{i c} f^2 (f+g x)^2 \left(-i d (f+g x)^n\right)^{-2/n} \text{Gamma}\left(\frac{2}{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} \text{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} \text{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} \text{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} \text{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} \text{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} \text{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} \text{Gamma}\left(\frac{4}{n},i d (f+g x)^n\right)}{2 g^4 n}+\frac{a x^4}{4}","\frac{3 i b e^{i c} f^2 (f+g x)^2 \left(-i d (f+g x)^n\right)^{-2/n} \text{Gamma}\left(\frac{2}{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} \text{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} \text{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} \text{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} \text{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} \text{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} \text{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} \text{Gamma}\left(\frac{4}{n},i d (f+g x)^n\right)}{2 g^4 n}+\frac{a x^4}{4}",1,"(a*x^4)/4 - ((I/2)*b*E^(I*c)*f^3*(f + g*x)*Gamma[n^(-1), (-I)*d*(f + g*x)^n])/(g^4*n*((-I)*d*(f + g*x)^n)^n^(-1)) + ((I/2)*b*f^3*(f + g*x)*Gamma[n^(-1), I*d*(f + g*x)^n])/(E^(I*c)*g^4*n*(I*d*(f + g*x)^n)^n^(-1)) + (((3*I)/2)*b*E^(I*c)*f^2*(f + g*x)^2*Gamma[2/n, (-I)*d*(f + g*x)^n])/(g^4*n*((-I)*d*(f + g*x)^n)^(2/n)) - (((3*I)/2)*b*f^2*(f + g*x)^2*Gamma[2/n, I*d*(f + g*x)^n])/(E^(I*c)*g^4*n*(I*d*(f + g*x)^n)^(2/n)) - (((3*I)/2)*b*E^(I*c)*f*(f + g*x)^3*Gamma[3/n, (-I)*d*(f + g*x)^n])/(g^4*n*((-I)*d*(f + g*x)^n)^(3/n)) + (((3*I)/2)*b*f*(f + g*x)^3*Gamma[3/n, I*d*(f + g*x)^n])/(E^(I*c)*g^4*n*(I*d*(f + g*x)^n)^(3/n)) + ((I/2)*b*E^(I*c)*(f + g*x)^4*Gamma[4/n, (-I)*d*(f + g*x)^n])/(g^4*n*((-I)*d*(f + g*x)^n)^(4/n)) - ((I/2)*b*(f + g*x)^4*Gamma[4/n, I*d*(f + g*x)^n])/(E^(I*c)*g^4*n*(I*d*(f + g*x)^n)^(4/n))","A",16,6,20,0.3000,1,"{14, 3433, 3365, 2208, 3423, 2218}"
267,1,383,0,0.3446958,"\int x^2 \left(a+b \sin \left(c+d (f+g x)^n\right)\right) \, dx","Int[x^2*(a + b*Sin[c + d*(f + g*x)^n]),x]","\frac{i b e^{i c} f^2 (f+g x) \left(-i d (f+g x)^n\right)^{-1/n} \text{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} \text{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} \text{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} \text{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} \text{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} \text{Gamma}\left(\frac{3}{n},i d (f+g x)^n\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} \text{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} \text{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} \text{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} \text{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} \text{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} \text{Gamma}\left(\frac{3}{n},i d (f+g x)^n\right)}{2 g^3 n}+\frac{a x^3}{3}",1,"(a*x^3)/3 + ((I/2)*b*E^(I*c)*f^2*(f + g*x)*Gamma[n^(-1), (-I)*d*(f + g*x)^n])/(g^3*n*((-I)*d*(f + g*x)^n)^n^(-1)) - ((I/2)*b*f^2*(f + g*x)*Gamma[n^(-1), I*d*(f + g*x)^n])/(E^(I*c)*g^3*n*(I*d*(f + g*x)^n)^n^(-1)) - (I*b*E^(I*c)*f*(f + g*x)^2*Gamma[2/n, (-I)*d*(f + g*x)^n])/(g^3*n*((-I)*d*(f + g*x)^n)^(2/n)) + (I*b*f*(f + g*x)^2*Gamma[2/n, I*d*(f + g*x)^n])/(E^(I*c)*g^3*n*(I*d*(f + g*x)^n)^(2/n)) + ((I/2)*b*E^(I*c)*(f + g*x)^3*Gamma[3/n, (-I)*d*(f + g*x)^n])/(g^3*n*((-I)*d*(f + g*x)^n)^(3/n)) - ((I/2)*b*(f + g*x)^3*Gamma[3/n, I*d*(f + g*x)^n])/(E^(I*c)*g^3*n*(I*d*(f + g*x)^n)^(3/n))","A",13,6,20,0.3000,1,"{14, 3433, 3365, 2208, 3423, 2218}"
268,1,255,0,0.1915205,"\int x \left(a+b \sin \left(c+d (f+g x)^n\right)\right) \, dx","Int[x*(a + b*Sin[c + d*(f + g*x)^n]),x]","\frac{i b e^{i c} (f+g x)^2 \left(-i d (f+g x)^n\right)^{-2/n} \text{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} \text{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} \text{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} \text{Gamma}\left(\frac{2}{n},i d (f+g x)^n\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} \text{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} \text{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} \text{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} \text{Gamma}\left(\frac{2}{n},i d (f+g x)^n\right)}{2 g^2 n}+\frac{a x^2}{2}",1,"(a*x^2)/2 - ((I/2)*b*E^(I*c)*f*(f + g*x)*Gamma[n^(-1), (-I)*d*(f + g*x)^n])/(g^2*n*((-I)*d*(f + g*x)^n)^n^(-1)) + ((I/2)*b*f*(f + g*x)*Gamma[n^(-1), I*d*(f + g*x)^n])/(E^(I*c)*g^2*n*(I*d*(f + g*x)^n)^n^(-1)) + ((I/2)*b*E^(I*c)*(f + g*x)^2*Gamma[2/n, (-I)*d*(f + g*x)^n])/(g^2*n*((-I)*d*(f + g*x)^n)^(2/n)) - ((I/2)*b*(f + g*x)^2*Gamma[2/n, I*d*(f + g*x)^n])/(E^(I*c)*g^2*n*(I*d*(f + g*x)^n)^(2/n))","A",10,6,18,0.3333,1,"{14, 3433, 3365, 2208, 3423, 2218}"
269,1,122,0,0.0579811,"\int \left(a+b \sin \left(c+d (f+g x)^n\right)\right) \, dx","Int[a + b*Sin[c + d*(f + g*x)^n],x]","\frac{i b e^{i c} (f+g x) \left(-i d (f+g x)^n\right)^{-1/n} \text{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} \text{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} \text{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} \text{Gamma}\left(\frac{1}{n},i d (f+g x)^n\right)}{2 g n}+a x",1,"a*x + ((I/2)*b*E^(I*c)*(f + g*x)*Gamma[n^(-1), (-I)*d*(f + g*x)^n])/(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])/(E^(I*c)*g*n*(I*d*(f + g*x)^n)^n^(-1))","A",4,2,16,0.1250,1,"{3365, 2208}"
270,0,0,0,0.018133,"\int \frac{a+b \sin \left(c+d (f+g x)^n\right)}{x} \, dx","Int[(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,"a*Log[x] + b*Defer[Int][Sin[c + d*(f + g*x)^n]/x, x]","A",0,0,0,0,-1,"{}"
271,0,0,0,0.0184941,"\int \frac{a+b \sin \left(c+d (f+g x)^n\right)}{x^2} \, dx","Int[(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,"-(a/x) + b*Defer[Int][Sin[c + d*(f + g*x)^n]/x^2, x]","A",0,0,0,0,-1,"{}"
272,1,856,0,0.9657018,"\int x^2 \left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2 \, dx","Int[x^2*(a + b*Sin[c + d*(f + g*x)^n])^2,x]","\frac{i a b e^{i c} (f+g x)^3 \text{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 \text{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 \text{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 \text{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) \text{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) \text{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} \text{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} \text{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} \text{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} \text{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} \text{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} \text{Gamma}\left(\frac{3}{n},2 i d (f+g x)^n\right)}{g^3 n}","\frac{i a b e^{i c} (f+g x)^3 \text{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 \text{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 \text{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 \text{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) \text{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) \text{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} \text{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} \text{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} \text{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} \text{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} \text{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} \text{Gamma}\left(\frac{3}{n},2 i d (f+g x)^n\right)}{g^3 n}",1,"((2*a^2 + b^2)*f^2*x)/(2*g^2) - ((2*a^2 + b^2)*f*(f + g*x)^2)/(2*g^3) + ((2*a^2 + b^2)*(f + g*x)^3)/(6*g^3) + (I*a*b*E^(I*c)*f^2*(f + g*x)*Gamma[n^(-1), (-I)*d*(f + g*x)^n])/(g^3*n*((-I)*d*(f + g*x)^n)^n^(-1)) - (I*a*b*f^2*(f + g*x)*Gamma[n^(-1), I*d*(f + g*x)^n])/(E^(I*c)*g^3*n*(I*d*(f + g*x)^n)^n^(-1)) + (2^(-2 - n^(-1))*b^2*E^((2*I)*c)*f^2*(f + g*x)*Gamma[n^(-1), (-2*I)*d*(f + g*x)^n])/(g^3*n*((-I)*d*(f + g*x)^n)^n^(-1)) + (2^(-2 - n^(-1))*b^2*f^2*(f + g*x)*Gamma[n^(-1), (2*I)*d*(f + g*x)^n])/(E^((2*I)*c)*g^3*n*(I*d*(f + g*x)^n)^n^(-1)) - ((2*I)*a*b*E^(I*c)*f*(f + g*x)^2*Gamma[2/n, (-I)*d*(f + g*x)^n])/(g^3*n*((-I)*d*(f + g*x)^n)^(2/n)) + ((2*I)*a*b*f*(f + g*x)^2*Gamma[2/n, I*d*(f + g*x)^n])/(E^(I*c)*g^3*n*(I*d*(f + g*x)^n)^(2/n)) - (2^(-1 - 2/n)*b^2*E^((2*I)*c)*f*(f + g*x)^2*Gamma[2/n, (-2*I)*d*(f + g*x)^n])/(g^3*n*((-I)*d*(f + g*x)^n)^(2/n)) - (2^(-1 - 2/n)*b^2*f*(f + g*x)^2*Gamma[2/n, (2*I)*d*(f + g*x)^n])/(E^((2*I)*c)*g^3*n*(I*d*(f + g*x)^n)^(2/n)) + (I*a*b*E^(I*c)*(f + g*x)^3*Gamma[3/n, (-I)*d*(f + g*x)^n])/(g^3*n*((-I)*d*(f + g*x)^n)^(3/n)) - (I*a*b*(f + g*x)^3*Gamma[3/n, I*d*(f + g*x)^n])/(E^(I*c)*g^3*n*(I*d*(f + g*x)^n)^(3/n)) + (2^(-2 - 3/n)*b^2*E^((2*I)*c)*(f + g*x)^3*Gamma[3/n, (-2*I)*d*(f + g*x)^n])/(g^3*n*((-I)*d*(f + g*x)^n)^(3/n)) + (2^(-2 - 3/n)*b^2*(f + g*x)^3*Gamma[3/n, (2*I)*d*(f + g*x)^n])/(E^((2*I)*c)*g^3*n*(I*d*(f + g*x)^n)^(3/n))","A",28,10,22,0.4545,1,"{3433, 3367, 3366, 2208, 3365, 3425, 6, 3424, 2218, 3423}"
273,1,556,0,0.4568118,"\int x \left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2 \, dx","Int[x*(a + b*Sin[c + d*(f + g*x)^n])^2,x]","\frac{i a b e^{i c} (f+g x)^2 \left(-i d (f+g x)^n\right)^{-2/n} \text{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} \text{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} \text{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} \text{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} \text{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} \text{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} \text{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} \text{Gamma}\left(\frac{2}{n},2 i d (f+g x)^n\right)}{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} \text{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} \text{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} \text{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} \text{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} \text{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} \text{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} \text{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} \text{Gamma}\left(\frac{2}{n},2 i d (f+g x)^n\right)}{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}",1,"-((2*a^2 + b^2)*f*x)/(2*g) + ((2*a^2 + b^2)*(f + g*x)^2)/(4*g^2) - (I*a*b*E^(I*c)*f*(f + g*x)*Gamma[n^(-1), (-I)*d*(f + g*x)^n])/(g^2*n*((-I)*d*(f + g*x)^n)^n^(-1)) + (I*a*b*f*(f + g*x)*Gamma[n^(-1), I*d*(f + g*x)^n])/(E^(I*c)*g^2*n*(I*d*(f + g*x)^n)^n^(-1)) - (2^(-2 - n^(-1))*b^2*E^((2*I)*c)*f*(f + g*x)*Gamma[n^(-1), (-2*I)*d*(f + g*x)^n])/(g^2*n*((-I)*d*(f + g*x)^n)^n^(-1)) - (2^(-2 - n^(-1))*b^2*f*(f + g*x)*Gamma[n^(-1), (2*I)*d*(f + g*x)^n])/(E^((2*I)*c)*g^2*n*(I*d*(f + g*x)^n)^n^(-1)) + (I*a*b*E^(I*c)*(f + g*x)^2*Gamma[2/n, (-I)*d*(f + g*x)^n])/(g^2*n*((-I)*d*(f + g*x)^n)^(2/n)) - (I*a*b*(f + g*x)^2*Gamma[2/n, I*d*(f + g*x)^n])/(E^(I*c)*g^2*n*(I*d*(f + g*x)^n)^(2/n)) + (4^(-1 - n^(-1))*b^2*E^((2*I)*c)*(f + g*x)^2*Gamma[2/n, (-2*I)*d*(f + g*x)^n])/(g^2*n*((-I)*d*(f + g*x)^n)^(2/n)) + (4^(-1 - n^(-1))*b^2*(f + g*x)^2*Gamma[2/n, (2*I)*d*(f + g*x)^n])/(E^((2*I)*c)*g^2*n*(I*d*(f + g*x)^n)^(2/n))","A",19,10,20,0.5000,1,"{3433, 3367, 3366, 2208, 3365, 3425, 6, 3424, 2218, 3423}"
274,1,261,0,0.1492131,"\int \left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2 \, dx","Int[(a + b*Sin[c + d*(f + g*x)^n])^2,x]","\frac{i a b e^{i c} (f+g x) \left(-i d (f+g x)^n\right)^{-1/n} \text{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} \text{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} \text{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} \text{Gamma}\left(\frac{1}{n},2 i d (f+g x)^n\right)}{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} \text{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} \text{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} \text{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} \text{Gamma}\left(\frac{1}{n},2 i d (f+g x)^n\right)}{g n}+\frac{1}{2} x \left(2 a^2+b^2\right)",1,"((2*a^2 + b^2)*x)/2 + (I*a*b*E^(I*c)*(f + g*x)*Gamma[n^(-1), (-I)*d*(f + g*x)^n])/(g*n*((-I)*d*(f + g*x)^n)^n^(-1)) - (I*a*b*(f + g*x)*Gamma[n^(-1), I*d*(f + g*x)^n])/(E^(I*c)*g*n*(I*d*(f + g*x)^n)^n^(-1)) + (2^(-2 - n^(-1))*b^2*E^((2*I)*c)*(f + g*x)*Gamma[n^(-1), (-2*I)*d*(f + g*x)^n])/(g*n*((-I)*d*(f + g*x)^n)^n^(-1)) + (2^(-2 - n^(-1))*b^2*(f + g*x)*Gamma[n^(-1), (2*I)*d*(f + g*x)^n])/(E^((2*I)*c)*g*n*(I*d*(f + g*x)^n)^n^(-1))","A",8,4,18,0.2222,1,"{3367, 3366, 2208, 3365}"
275,0,0,0,0.024356,"\int \frac{\left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2}{x} \, dx","Int[(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,"Defer[Int][(a + b*Sin[c + d*(f + g*x)^n])^2/x, x]","A",0,0,0,0,-1,"{}"
276,0,0,0,0.0255086,"\int \frac{\left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2}{x^2} \, dx","Int[(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,"Defer[Int][(a + b*Sin[c + d*(f + g*x)^n])^2/x^2, x]","A",0,0,0,0,-1,"{}"
277,0,0,0,0.0275613,"\int \frac{x^2}{a+b \sin \left(c+d (f+g x)^n\right)} \, dx","Int[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,"Defer[Int][x^2/(a + b*Sin[c + d*(f + g*x)^n]), x]","A",0,0,0,0,-1,"{}"
278,0,0,0,0.0183274,"\int \frac{x}{a+b \sin \left(c+d (f+g x)^n\right)} \, dx","Int[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,"Defer[Int][x/(a + b*Sin[c + d*(f + g*x)^n]), x]","A",0,0,0,0,-1,"{}"
279,0,0,0,0.0056604,"\int \frac{1}{a+b \sin \left(c+d (f+g x)^n\right)} \, dx","Int[(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,"Defer[Int][(a + b*Sin[c + d*(f + g*x)^n])^(-1), x]","A",0,0,0,0,-1,"{}"
280,0,0,0,0.0274813,"\int \frac{1}{x \left(a+b \sin \left(c+d (f+g x)^n\right)\right)} \, dx","Int[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,"Defer[Int][1/(x*(a + b*Sin[c + d*(f + g*x)^n])), x]","A",0,0,0,0,-1,"{}"
281,0,0,0,0.0274604,"\int \frac{1}{x^2 \left(a+b \sin \left(c+d (f+g x)^n\right)\right)} \, dx","Int[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,"Defer[Int][1/(x^2*(a + b*Sin[c + d*(f + g*x)^n])), x]","A",0,0,0,0,-1,"{}"
282,0,0,0,0.0274452,"\int \frac{x^2}{\left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2} \, dx","Int[x^2/(a + b*Sin[c + d*(f + g*x)^n])^2,x]","\int \frac{x^2}{\left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2} \, dx","\text{Int}\left(\frac{x^2}{\left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2},x\right)",0,"Defer[Int][x^2/(a + b*Sin[c + d*(f + g*x)^n])^2, x]","A",0,0,0,0,-1,"{}"
283,0,0,0,0.0145726,"\int \frac{x}{\left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2} \, dx","Int[x/(a + b*Sin[c + d*(f + g*x)^n])^2,x]","\int \frac{x}{\left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2} \, dx","\text{Int}\left(\frac{x}{\left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2},x\right)",0,"Defer[Int][x/(a + b*Sin[c + d*(f + g*x)^n])^2, x]","A",0,0,0,0,-1,"{}"
284,0,0,0,0.005769,"\int \frac{1}{\left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2} \, dx","Int[(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,"Defer[Int][(a + b*Sin[c + d*(f + g*x)^n])^(-2), x]","A",0,0,0,0,-1,"{}"
285,0,0,0,0.0261045,"\int \frac{1}{x \left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2} \, dx","Int[1/(x*(a + b*Sin[c + d*(f + g*x)^n])^2),x]","\int \frac{1}{x \left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x \left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2},x\right)",0,"Defer[Int][1/(x*(a + b*Sin[c + d*(f + g*x)^n])^2), x]","A",0,0,0,0,-1,"{}"
286,0,0,0,0.0256077,"\int \frac{1}{x^2 \left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2} \, dx","Int[1/(x^2*(a + b*Sin[c + d*(f + g*x)^n])^2),x]","\int \frac{1}{x^2 \left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{x^2 \left(a+b \sin \left(c+d (f+g x)^n\right)\right)^2},x\right)",0,"Defer[Int][1/(x^2*(a + b*Sin[c + d*(f + g*x)^n])^2), x]","A",0,0,0,0,-1,"{}"
287,0,0,0,0.0239176,"\int (e x)^m \left(a+b \sin \left(c+d (f+g x)^n\right)\right)^p \, dx","Int[(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,"Defer[Int][(e*x)^m*(a + b*Sin[c + d*(f + g*x)^n])^p, x]","A",0,0,0,0,-1,"{}"
288,1,224,0,0.4570953,"\int (e+f x)^2 \left(a+b \sin \left(c+\frac{d}{x}\right)\right) \, dx","Int[(e + f*x)^2*(a + b*Sin[c + d/x]),x]","a e^2 x+a e f x^2+\frac{1}{3} a f^2 x^3+b d^2 e f \sin (c) \text{CosIntegral}\left(\frac{d}{x}\right)+\frac{1}{6} b d^3 f^2 \cos (c) \text{CosIntegral}\left(\frac{d}{x}\right)-b d e^2 \cos (c) \text{CosIntegral}\left(\frac{d}{x}\right)+b d^2 e f \cos (c) \text{Si}\left(\frac{d}{x}\right)-\frac{1}{6} b d^3 f^2 \sin (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)","a e^2 x+a e f x^2+\frac{1}{3} a f^2 x^3+b d^2 e f \sin (c) \text{CosIntegral}\left(\frac{d}{x}\right)+\frac{1}{6} b d^3 f^2 \cos (c) \text{CosIntegral}\left(\frac{d}{x}\right)-b d e^2 \cos (c) \text{CosIntegral}\left(\frac{d}{x}\right)+b d^2 e f \cos (c) \text{Si}\left(\frac{d}{x}\right)-\frac{1}{6} b d^3 f^2 \sin (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,"a*e^2*x + a*e*f*x^2 + (a*f^2*x^3)/3 + b*d*e*f*x*Cos[c + d/x] + (b*d*f^2*x^2*Cos[c + d/x])/6 - b*d*e^2*Cos[c]*CosIntegral[d/x] + (b*d^3*f^2*Cos[c]*CosIntegral[d/x])/6 + b*d^2*e*f*CosIntegral[d/x]*Sin[c] + b*e^2*x*Sin[c + d/x] - (b*d^2*f^2*x*Sin[c + d/x])/6 + b*e*f*x^2*Sin[c + d/x] + (b*f^2*x^3*Sin[c + d/x])/3 + b*d^2*e*f*Cos[c]*SinIntegral[d/x] + b*d*e^2*Sin[c]*SinIntegral[d/x] - (b*d^3*f^2*Sin[c]*SinIntegral[d/x])/6","A",23,6,20,0.3000,1,"{3431, 14, 3297, 3303, 3299, 3302}"
289,1,118,0,0.2391249,"\int (e+f x) \left(a+b \sin \left(c+\frac{d}{x}\right)\right) \, dx","Int[(e + f*x)*(a + b*Sin[c + d/x]),x]","a e x+\frac{1}{2} a f x^2+\frac{1}{2} b d^2 f \sin (c) \text{CosIntegral}\left(\frac{d}{x}\right)-b d e \cos (c) \text{CosIntegral}\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)","a e x+\frac{1}{2} a f x^2+\frac{1}{2} b d^2 f \sin (c) \text{CosIntegral}\left(\frac{d}{x}\right)-b d e \cos (c) \text{CosIntegral}\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,"a*e*x + (a*f*x^2)/2 + (b*d*f*x*Cos[c + d/x])/2 - b*d*e*Cos[c]*CosIntegral[d/x] + (b*d^2*f*CosIntegral[d/x]*Sin[c])/2 + b*e*x*Sin[c + d/x] + (b*f*x^2*Sin[c + d/x])/2 + (b*d^2*f*Cos[c]*SinIntegral[d/x])/2 + b*d*e*Sin[c]*SinIntegral[d/x]","A",15,6,18,0.3333,1,"{3431, 14, 3297, 3303, 3299, 3302}"
290,1,38,0,0.0783685,"\int \left(a+b \sin \left(c+\frac{d}{x}\right)\right) \, dx","Int[a + b*Sin[c + d/x],x]","a x-b d \cos (c) \text{CosIntegral}\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)","a x-b d \cos (c) \text{CosIntegral}\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*d*Cos[c]*CosIntegral[d/x] + b*x*Sin[c + d/x] + b*d*Sin[c]*SinIntegral[d/x]","A",6,5,12,0.4167,1,"{3361, 3297, 3303, 3299, 3302}"
291,1,103,0,0.2785746,"\int \frac{a+b \sin \left(c+\frac{d}{x}\right)}{e+f x} \, dx","Int[(a + b*Sin[c + d/x])/(e + f*x),x]","\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{CosIntegral}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right)}{f}-\frac{b \sin (c) \text{CosIntegral}\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}","\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{CosIntegral}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right)}{f}-\frac{b \sin (c) \text{CosIntegral}\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[f + e/x])/f + (a*Log[x])/f - (b*CosIntegral[d/x]*Sin[c])/f + (b*CosIntegral[d*(f/e + x^(-1))]*Sin[c - (d*f)/e])/f + (b*Cos[c - (d*f)/e]*SinIntegral[d*(f/e + x^(-1))])/f - (b*Cos[c]*SinIntegral[d/x])/f","A",12,6,20,0.3000,1,"{3431, 14, 3303, 3299, 3302, 3317}"
292,1,94,0,0.2218758,"\int \frac{a+b \sin \left(c+\frac{d}{x}\right)}{(e+f x)^2} \, dx","Int[(a + b*Sin[c + d/x])/(e + f*x)^2,x]","\frac{a}{e \left(\frac{e}{x}+f\right)}-\frac{b d \cos \left(c-\frac{d f}{e}\right) \text{CosIntegral}\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)}","\frac{a}{e \left(\frac{e}{x}+f\right)}-\frac{b d \cos \left(c-\frac{d f}{e}\right) \text{CosIntegral}\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,"a/(e*(f + e/x)) - (b*d*Cos[c - (d*f)/e]*CosIntegral[d*(f/e + x^(-1))])/e^2 + (b*Sin[c + d/x])/(e*(f + e/x)) + (b*d*Sin[c - (d*f)/e]*SinIntegral[d*(f/e + x^(-1))])/e^2","A",7,6,20,0.3000,1,"{3431, 3317, 3297, 3303, 3299, 3302}"
293,1,233,0,0.4874388,"\int \frac{a+b \sin \left(c+\frac{d}{x}\right)}{(e+f x)^3} \, dx","Int[(a + b*Sin[c + d/x])/(e + f*x)^3,x]","\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{CosIntegral}\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{CosIntegral}\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 \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}-\frac{b d f \cos \left(c+\frac{d}{x}\right)}{2 e^3 \left(\frac{e}{x}+f\right)}","\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{CosIntegral}\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{CosIntegral}\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 \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}-\frac{b d f \cos \left(c+\frac{d}{x}\right)}{2 e^3 \left(\frac{e}{x}+f\right)}",1,"-(a*f)/(2*e^2*(f + e/x)^2) + a/(e^2*(f + e/x)) - (b*d*f*Cos[c + d/x])/(2*e^3*(f + e/x)) - (b*d*Cos[c - (d*f)/e]*CosIntegral[d*(f/e + x^(-1))])/e^3 - (b*d^2*f*CosIntegral[d*(f/e + x^(-1))]*Sin[c - (d*f)/e])/(2*e^4) - (b*f*Sin[c + d/x])/(2*e^2*(f + e/x)^2) + (b*Sin[c + d/x])/(e^2*(f + e/x)) - (b*d^2*f*Cos[c - (d*f)/e]*SinIntegral[d*(f/e + x^(-1))])/(2*e^4) + (b*d*Sin[c - (d*f)/e]*SinIntegral[d*(f/e + x^(-1))])/e^3","A",15,6,20,0.3000,1,"{3431, 3317, 3297, 3303, 3299, 3302}"
294,1,254,0,0.6160034,"\int (e+f x) \left(a+b \sin \left(c+\frac{d}{x}\right)\right)^2 \, dx","Int[(e + f*x)*(a + b*Sin[c + d/x])^2,x]","a^2 e x+\frac{1}{2} a^2 f x^2+a b d^2 f \sin (c) \text{CosIntegral}\left(\frac{d}{x}\right)-2 a b d e \cos (c) \text{CosIntegral}\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{CosIntegral}\left(\frac{2 d}{x}\right)-b^2 d e \sin (2 c) \text{CosIntegral}\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)","a^2 e x+\frac{1}{2} a^2 f x^2+a b d^2 f \sin (c) \text{CosIntegral}\left(\frac{d}{x}\right)-2 a b d e \cos (c) \text{CosIntegral}\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{CosIntegral}\left(\frac{2 d}{x}\right)-b^2 d e \sin (2 c) \text{CosIntegral}\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,"a^2*e*x + (a^2*f*x^2)/2 + a*b*d*f*x*Cos[c + d/x] - 2*a*b*d*e*Cos[c]*CosIntegral[d/x] - b^2*d^2*f*Cos[2*c]*CosIntegral[(2*d)/x] + a*b*d^2*f*CosIntegral[d/x]*Sin[c] - b^2*d*e*CosIntegral[(2*d)/x]*Sin[2*c] + 2*a*b*e*x*Sin[c + d/x] + a*b*f*x^2*Sin[c + d/x] + b^2*d*f*x*Cos[c + d/x]*Sin[c + d/x] + b^2*e*x*Sin[c + d/x]^2 + (b^2*f*x^2*Sin[c + d/x]^2)/2 + a*b*d^2*f*Cos[c]*SinIntegral[d/x] + 2*a*b*d*e*Sin[c]*SinIntegral[d/x] - b^2*d*e*Cos[2*c]*SinIntegral[(2*d)/x] + b^2*d^2*f*Sin[2*c]*SinIntegral[(2*d)/x]","A",27,11,20,0.5500,1,"{3431, 3317, 3297, 3303, 3299, 3302, 3314, 29, 3312, 3313, 12}"
295,1,94,0,0.2263497,"\int \left(a+b \sin \left(c+\frac{d}{x}\right)\right)^2 \, dx","Int[(a + b*Sin[c + d/x])^2,x]","a^2 x-2 a b d \cos (c) \text{CosIntegral}\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{CosIntegral}\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)","a^2 x-2 a b d \cos (c) \text{CosIntegral}\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{CosIntegral}\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,"a^2*x - 2*a*b*d*Cos[c]*CosIntegral[d/x] - b^2*d*CosIntegral[(2*d)/x]*Sin[2*c] + 2*a*b*x*Sin[c + d/x] + b^2*x*Sin[c + d/x]^2 + 2*a*b*d*Sin[c]*SinIntegral[d/x] - b^2*d*Cos[2*c]*SinIntegral[(2*d)/x]","A",12,8,14,0.5714,1,"{3361, 3317, 3297, 3303, 3299, 3302, 3313, 12}"
296,1,255,0,0.6627602,"\int \frac{\left(a+b \sin \left(c+\frac{d}{x}\right)\right)^2}{e+f x} \, dx","Int[(a + b*Sin[c + d/x])^2/(e + f*x),x]","\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{CosIntegral}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right)}{f}-\frac{2 a b \sin (c) \text{CosIntegral}\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{CosIntegral}\left(2 d \left(\frac{f}{e}+\frac{1}{x}\right)\right)}{2 f}+\frac{b^2 \cos (2 c) \text{CosIntegral}\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}","\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{CosIntegral}\left(d \left(\frac{f}{e}+\frac{1}{x}\right)\right)}{f}-\frac{2 a b \sin (c) \text{CosIntegral}\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{CosIntegral}\left(2 d \left(\frac{f}{e}+\frac{1}{x}\right)\right)}{2 f}+\frac{b^2 \cos (2 c) \text{CosIntegral}\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))])/(2*f) + (b^2*Cos[2*c]*CosIntegral[(2*d)/x])/(2*f) + (a^2*Log[f + e/x])/f + (b^2*Log[f + e/x])/(2*f) + (a^2*Log[x])/f + (b^2*Log[x])/(2*f) - (2*a*b*CosIntegral[d/x]*Sin[c])/f + (2*a*b*CosIntegral[d*(f/e + x^(-1))]*Sin[c - (d*f)/e])/f + (2*a*b*Cos[c - (d*f)/e]*SinIntegral[d*(f/e + x^(-1))])/f + (b^2*Sin[2*c - (2*d*f)/e]*SinIntegral[2*d*(f/e + x^(-1))])/(2*f) - (2*a*b*Cos[c]*SinIntegral[d/x])/f - (b^2*Sin[2*c]*SinIntegral[(2*d)/x])/(2*f)","A",22,6,22,0.2727,1,"{3431, 3317, 3303, 3299, 3302, 3312}"
297,1,195,0,0.3910293,"\int \frac{\left(a+b \sin \left(c+\frac{d}{x}\right)\right)^2}{(e+f x)^2} \, dx","Int[(a + b*Sin[c + d/x])^2/(e + f*x)^2,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{CosIntegral}\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{CosIntegral}\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)}","\frac{a^2}{e \left(\frac{e}{x}+f\right)}-\frac{2 a b d \cos \left(c-\frac{d f}{e}\right) \text{CosIntegral}\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{CosIntegral}\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,"a^2/(e*(f + e/x)) - (2*a*b*d*Cos[c - (d*f)/e]*CosIntegral[d*(f/e + x^(-1))])/e^2 - (b^2*d*CosIntegral[2*d*(f/e + x^(-1))]*Sin[2*c - (2*d*f)/e])/e^2 + (2*a*b*Sin[c + d/x])/(e*(f + e/x)) + (b^2*Sin[c + d/x]^2)/(e*(f + e/x)) + (2*a*b*d*Sin[c - (d*f)/e]*SinIntegral[d*(f/e + x^(-1))])/e^2 - (b^2*d*Cos[2*c - (2*d*f)/e]*SinIntegral[2*d*(f/e + x^(-1))])/e^2","A",12,8,22,0.3636,1,"{3431, 3317, 3297, 3303, 3299, 3302, 3313, 12}"
298,1,470,0,0.9572615,"\int \frac{\left(a+b \sin \left(c+\frac{d}{x}\right)\right)^2}{(e+f x)^3} \, dx","Int[(a + b*Sin[c + d/x])^2/(e + f*x)^3,x]","\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{CosIntegral}\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{CosIntegral}\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{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{a b d f \cos \left(c+\frac{d}{x}\right)}{e^3 \left(\frac{e}{x}+f\right)}+\frac{b^2 d^2 f \cos \left(2 c-\frac{2 d f}{e}\right) \text{CosIntegral}\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{CosIntegral}\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 \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}-\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{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{CosIntegral}\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{CosIntegral}\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{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{a b d f \cos \left(c+\frac{d}{x}\right)}{e^3 \left(\frac{e}{x}+f\right)}+\frac{b^2 d^2 f \cos \left(2 c-\frac{2 d f}{e}\right) \text{CosIntegral}\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{CosIntegral}\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 \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}-\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)}",1,"-(a^2*f)/(2*e^2*(f + e/x)^2) + a^2/(e^2*(f + e/x)) - (a*b*d*f*Cos[c + d/x])/(e^3*(f + e/x)) - (2*a*b*d*Cos[c - (d*f)/e]*CosIntegral[d*(f/e + x^(-1))])/e^3 + (b^2*d^2*f*Cos[2*c - (2*d*f)/e]*CosIntegral[2*d*(f/e + x^(-1))])/e^4 - (b^2*d*CosIntegral[2*d*(f/e + x^(-1))]*Sin[2*c - (2*d*f)/e])/e^3 - (a*b*d^2*f*CosIntegral[d*(f/e + x^(-1))]*Sin[c - (d*f)/e])/e^4 - (a*b*f*Sin[c + d/x])/(e^2*(f + e/x)^2) + (2*a*b*Sin[c + d/x])/(e^2*(f + e/x)) - (b^2*d*f*Cos[c + d/x]*Sin[c + d/x])/(e^3*(f + e/x)) - (b^2*f*Sin[c + d/x]^2)/(2*e^2*(f + e/x)^2) + (b^2*Sin[c + d/x]^2)/(e^2*(f + e/x)) - (a*b*d^2*f*Cos[c - (d*f)/e]*SinIntegral[d*(f/e + x^(-1))])/e^4 + (2*a*b*d*Sin[c - (d*f)/e]*SinIntegral[d*(f/e + x^(-1))])/e^3 - (b^2*d*Cos[2*c - (2*d*f)/e]*SinIntegral[2*d*(f/e + x^(-1))])/e^3 - (b^2*d^2*f*Sin[2*c - (2*d*f)/e]*SinIntegral[2*d*(f/e + x^(-1))])/e^4","A",27,11,22,0.5000,1,"{3431, 3317, 3297, 3303, 3299, 3302, 3314, 31, 3312, 3313, 12}"
299,0,0,0,0.031669,"\int \frac{(e+f x)^2}{a+b \sin \left(c+\frac{d}{x}\right)} \, dx","Int[(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,"Defer[Int][(e + f*x)^2/(a + b*Sin[c + d/x]), x]","A",0,0,0,0,-1,"{}"
300,0,0,0,0.017325,"\int \frac{e+f x}{a+b \sin \left(c+\frac{d}{x}\right)} \, dx","Int[(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,"Defer[Int][(e + f*x)/(a + b*Sin[c + d/x]), x]","A",0,0,0,0,-1,"{}"
301,0,0,0,0.0051691,"\int \frac{1}{a+b \sin \left(c+\frac{d}{x}\right)} \, dx","Int[(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,"Defer[Int][(a + b*Sin[c + d/x])^(-1), x]","A",0,0,0,0,-1,"{}"
302,0,0,0,0.0172068,"\int \frac{e+f x}{a+b \sin \left(c+\frac{d}{x}\right)} \, dx","Int[(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,"Defer[Int][(e + f*x)/(a + b*Sin[c + d/x]), x]","A",0,0,0,0,-1,"{}"
303,0,0,0,0.0314051,"\int \frac{(e+f x)^2}{a+b \sin \left(c+\frac{d}{x}\right)} \, dx","Int[(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,"Defer[Int][(e + f*x)^2/(a + b*Sin[c + d/x]), x]","A",0,0,0,0,-1,"{}"
304,0,0,0,0.0295132,"\int \frac{(e+f x)^2}{\left(a+b \sin \left(c+\frac{d}{x}\right)\right)^2} \, dx","Int[(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,"Defer[Int][(e + f*x)^2/(a + b*Sin[c + d/x])^2, x]","A",0,0,0,0,-1,"{}"
305,0,0,0,0.0165308,"\int \frac{e+f x}{\left(a+b \sin \left(c+\frac{d}{x}\right)\right)^2} \, dx","Int[(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,"Defer[Int][(e + f*x)/(a + b*Sin[c + d/x])^2, x]","A",0,0,0,0,-1,"{}"
306,0,0,0,0.0052627,"\int \frac{1}{\left(a+b \sin \left(c+\frac{d}{x}\right)\right)^2} \, dx","Int[(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,"Defer[Int][(a + b*Sin[c + d/x])^(-2), x]","A",0,0,0,0,-1,"{}"
307,0,0,0,0.0158103,"\int \frac{e+f x}{\left(a+b \sin \left(c+\frac{d}{x}\right)\right)^2} \, dx","Int[(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,"Defer[Int][(e + f*x)/(a + b*Sin[c + d/x])^2, x]","A",0,0,0,0,-1,"{}"
308,0,0,0,0.0302505,"\int \frac{(e+f x)^2}{\left(a+b \sin \left(c+\frac{d}{x}\right)\right)^2} \, dx","Int[(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,"Defer[Int][(e + f*x)^2/(a + b*Sin[c + d/x])^2, x]","A",0,0,0,0,-1,"{}"
309,0,0,0,0.0279417,"\int (e+f x)^m \left(a+b \sin \left(c+\frac{d}{x}\right)\right)^p \, dx","Int[(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,"Defer[Int][(e + f*x)^m*(a + b*Sin[c + d/x])^p, x]","A",0,0,0,0,-1,"{}"
310,1,115,0,0.2873025,"\int x^m \sqrt[3]{c \sin ^3(a+b x)} \, dx","Int[x^m*(c*Sin[a + b*x]^3)^(1/3),x]","-\frac{e^{i a} x^m (-i b x)^{-m} \csc (a+b x) \text{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) \text{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) \text{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) \text{Gamma}(m+1,i b x) \sqrt[3]{c \sin ^3(a+b x)}}{2 b}",1,"-(E^(I*a)*x^m*Csc[a + b*x]*Gamma[1 + m, (-I)*b*x]*(c*Sin[a + b*x]^3)^(1/3))/(2*b*((-I)*b*x)^m) - (x^m*Csc[a + b*x]*Gamma[1 + m, I*b*x]*(c*Sin[a + b*x]^3)^(1/3))/(2*b*E^(I*a)*(I*b*x)^m)","A",4,3,18,0.1667,1,"{6720, 3308, 2181}"
311,1,96,0,0.207996,"\int x^3 \sqrt[3]{c \sin ^3(a+b x)} \, dx","Int[x^3*(c*Sin[a + b*x]^3)^(1/3),x]","\frac{3 x^2 \sqrt[3]{c \sin ^3(a+b x)}}{b^2}-\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{x^3 \cot (a+b x) \sqrt[3]{c \sin ^3(a+b x)}}{b}","\frac{3 x^2 \sqrt[3]{c \sin ^3(a+b x)}}{b^2}-\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{x^3 \cot (a+b x) \sqrt[3]{c \sin ^3(a+b x)}}{b}",1,"(-6*(c*Sin[a + b*x]^3)^(1/3))/b^4 + (3*x^2*(c*Sin[a + b*x]^3)^(1/3))/b^2 + (6*x*Cot[a + b*x]*(c*Sin[a + b*x]^3)^(1/3))/b^3 - (x^3*Cot[a + b*x]*(c*Sin[a + b*x]^3)^(1/3))/b","A",5,3,18,0.1667,1,"{6720, 3296, 2637}"
312,1,74,0,0.1820984,"\int x^2 \sqrt[3]{c \sin ^3(a+b x)} \, dx","Int[x^2*(c*Sin[a + b*x]^3)^(1/3),x]","\frac{2 x \sqrt[3]{c \sin ^3(a+b x)}}{b^2}+\frac{2 \cot (a+b x) \sqrt[3]{c \sin ^3(a+b x)}}{b^3}-\frac{x^2 \cot (a+b x) \sqrt[3]{c \sin ^3(a+b x)}}{b}","\frac{2 x \sqrt[3]{c \sin ^3(a+b x)}}{b^2}+\frac{2 \cot (a+b x) \sqrt[3]{c \sin ^3(a+b x)}}{b^3}-\frac{x^2 \cot (a+b x) \sqrt[3]{c \sin ^3(a+b x)}}{b}",1,"(2*x*(c*Sin[a + b*x]^3)^(1/3))/b^2 + (2*Cot[a + b*x]*(c*Sin[a + b*x]^3)^(1/3))/b^3 - (x^2*Cot[a + b*x]*(c*Sin[a + b*x]^3)^(1/3))/b","A",4,3,18,0.1667,1,"{6720, 3296, 2638}"
313,1,45,0,0.1273888,"\int x \sqrt[3]{c \sin ^3(a+b x)} \, dx","Int[x*(c*Sin[a + b*x]^3)^(1/3),x]","\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}","\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,"(c*Sin[a + b*x]^3)^(1/3)/b^2 - (x*Cot[a + b*x]*(c*Sin[a + b*x]^3)^(1/3))/b","A",3,3,16,0.1875,1,"{6720, 3296, 2637}"
314,1,25,0,0.0175031,"\int \sqrt[3]{c \sin ^3(a+b x)} \, dx","Int[(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",2,2,14,0.1429,1,"{3207, 2638}"
315,1,55,0,0.1657925,"\int \frac{\sqrt[3]{c \sin ^3(a+b x)}}{x} \, dx","Int[(c*Sin[a + b*x]^3)^(1/3)/x,x]","\sin (a) \text{CosIntegral}(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)}","\sin (a) \text{CosIntegral}(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,"CosIntegral[b*x]*Csc[a + b*x]*Sin[a]*(c*Sin[a + b*x]^3)^(1/3) + Cos[a]*Csc[a + b*x]*(c*Sin[a + b*x]^3)^(1/3)*SinIntegral[b*x]","A",4,4,18,0.2222,1,"{6720, 3303, 3299, 3302}"
316,1,77,0,0.1767342,"\int \frac{\sqrt[3]{c \sin ^3(a+b x)}}{x^2} \, dx","Int[(c*Sin[a + b*x]^3)^(1/3)/x^2,x]","b \cos (a) \text{CosIntegral}(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}","b \cos (a) \text{CosIntegral}(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)/x) + b*Cos[a]*CosIntegral[b*x]*Csc[a + b*x]*(c*Sin[a + b*x]^3)^(1/3) - b*Csc[a + b*x]*Sin[a]*(c*Sin[a + b*x]^3)^(1/3)*SinIntegral[b*x]","A",5,5,18,0.2778,1,"{6720, 3297, 3303, 3299, 3302}"
317,1,116,0,0.2055763,"\int \frac{\sqrt[3]{c \sin ^3(a+b x)}}{x^3} \, dx","Int[(c*Sin[a + b*x]^3)^(1/3)/x^3,x]","-\frac{1}{2} b^2 \sin (a) \text{CosIntegral}(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}","-\frac{1}{2} b^2 \sin (a) \text{CosIntegral}(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,"-(c*Sin[a + b*x]^3)^(1/3)/(2*x^2) - (b*Cot[a + b*x]*(c*Sin[a + b*x]^3)^(1/3))/(2*x) - (b^2*CosIntegral[b*x]*Csc[a + b*x]*Sin[a]*(c*Sin[a + b*x]^3)^(1/3))/2 - (b^2*Cos[a]*Csc[a + b*x]*(c*Sin[a + b*x]^3)^(1/3)*SinIntegral[b*x])/2","A",6,5,18,0.2778,1,"{6720, 3297, 3303, 3299, 3302}"
318,1,153,0,0.3013273,"\int x^m \sqrt[3]{c \sin ^3\left(a+b x^2\right)} \, dx","Int[x^m*(c*Sin[a + b*x^2]^3)^(1/3),x]","\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) \text{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) \text{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) \text{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) \text{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)*E^(I*a)*x^(1 + m)*((-I)*b*x^2)^((-1 - m)/2)*Csc[a + b*x^2]*Gamma[(1 + m)/2, (-I)*b*x^2]*(c*Sin[a + b*x^2]^3)^(1/3) - ((I/4)*x^(1 + m)*(I*b*x^2)^((-1 - m)/2)*Csc[a + b*x^2]*Gamma[(1 + m)/2, I*b*x^2]*(c*Sin[a + b*x^2]^3)^(1/3))/E^(I*a)","A",4,3,20,0.1500,1,"{6720, 3389, 2218}"
319,1,58,0,0.181158,"\int x^3 \sqrt[3]{c \sin ^3\left(a+b x^2\right)} \, dx","Int[x^3*(c*Sin[a + b*x^2]^3)^(1/3),x]","\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}","\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,"(c*Sin[a + b*x^2]^3)^(1/3)/(2*b^2) - (x^2*Cot[a + b*x^2]*(c*Sin[a + b*x^2]^3)^(1/3))/(2*b)","A",4,4,20,0.2000,1,"{6720, 3379, 3296, 2637}"
320,1,155,0,0.2144996,"\int x^2 \sqrt[3]{c \sin ^3\left(a+b x^2\right)} \, dx","Int[x^2*(c*Sin[a + b*x^2]^3)^(1/3),x]","\frac{\sqrt{\frac{\pi }{2}} \cos (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} 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}","\frac{\sqrt{\frac{\pi }{2}} \cos (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} 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,"-(x*Cot[a + b*x^2]*(c*Sin[a + b*x^2]^3)^(1/3))/(2*b) + (Sqrt[Pi/2]*Cos[a]*Csc[a + b*x^2]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x]*(c*Sin[a + b*x^2]^3)^(1/3))/(2*b^(3/2)) - (Sqrt[Pi/2]*Csc[a + b*x^2]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x]*Sin[a]*(c*Sin[a + b*x^2]^3)^(1/3))/(2*b^(3/2))","A",5,5,20,0.2500,1,"{6720, 3385, 3354, 3352, 3351}"
321,1,31,0,0.104194,"\int x \sqrt[3]{c \sin ^3\left(a+b x^2\right)} \, dx","Int[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,"-(Cot[a + b*x^2]*(c*Sin[a + b*x^2]^3)^(1/3))/(2*b)","A",3,3,18,0.1667,1,"{6715, 3207, 2638}"
322,1,117,0,0.0586227,"\int \sqrt[3]{c \sin ^3\left(a+b x^2\right)} \, dx","Int[(c*Sin[a + b*x^2]^3)^(1/3),x]","\frac{\sqrt{\frac{\pi }{2}} \sin (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} 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}}","\frac{\sqrt{\frac{\pi }{2}} \sin (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} 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]*Cos[a]*Csc[a + b*x^2]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x]*(c*Sin[a + b*x^2]^3)^(1/3))/Sqrt[b] + (Sqrt[Pi/2]*Csc[a + b*x^2]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x]*Sin[a]*(c*Sin[a + b*x^2]^3)^(1/3))/Sqrt[b]","A",4,4,16,0.2500,1,"{6720, 3353, 3352, 3351}"
323,1,73,0,0.1209851,"\int \frac{\sqrt[3]{c \sin ^3\left(a+b x^2\right)}}{x} \, dx","Int[(c*Sin[a + b*x^2]^3)^(1/3)/x,x]","\frac{1}{2} \sin (a) \text{CosIntegral}\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)}","\frac{1}{2} \sin (a) \text{CosIntegral}\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,"(CosIntegral[b*x^2]*Csc[a + b*x^2]*Sin[a]*(c*Sin[a + b*x^2]^3)^(1/3))/2 + (Cos[a]*Csc[a + b*x^2]*(c*Sin[a + b*x^2]^3)^(1/3)*SinIntegral[b*x^2])/2","A",4,4,20,0.2000,1,"{6720, 3377, 3376, 3375}"
324,1,135,0,0.1564097,"\int \frac{\sqrt[3]{c \sin ^3\left(a+b x^2\right)}}{x^2} \, dx","Int[(c*Sin[a + b*x^2]^3)^(1/3)/x^2,x]","\sqrt{2 \pi } \sqrt{b} \cos (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} 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}","\sqrt{2 \pi } \sqrt{b} \cos (a) \text{FresnelC}\left(\sqrt{\frac{2}{\pi }} \sqrt{b} 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,"-((c*Sin[a + b*x^2]^3)^(1/3)/x) + Sqrt[b]*Sqrt[2*Pi]*Cos[a]*Csc[a + b*x^2]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x]*(c*Sin[a + b*x^2]^3)^(1/3) - Sqrt[b]*Sqrt[2*Pi]*Csc[a + b*x^2]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x]*Sin[a]*(c*Sin[a + b*x^2]^3)^(1/3)","A",5,5,20,0.2500,1,"{6720, 3387, 3354, 3352, 3351}"
325,1,98,0,0.20267,"\int \frac{\sqrt[3]{c \sin ^3\left(a+b x^2\right)}}{x^3} \, dx","Int[(c*Sin[a + b*x^2]^3)^(1/3)/x^3,x]","\frac{1}{2} b \cos (a) \text{CosIntegral}\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}","\frac{1}{2} b \cos (a) \text{CosIntegral}\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,"-(c*Sin[a + b*x^2]^3)^(1/3)/(2*x^2) + (b*Cos[a]*CosIntegral[b*x^2]*Csc[a + b*x^2]*(c*Sin[a + b*x^2]^3)^(1/3))/2 - (b*Csc[a + b*x^2]*Sin[a]*(c*Sin[a + b*x^2]^3)^(1/3)*SinIntegral[b*x^2])/2","A",6,6,20,0.3000,1,"{6720, 3379, 3297, 3303, 3299, 3302}"
326,1,157,0,0.3805591,"\int x^m \sqrt[3]{c \sin ^3\left(a+b x^n\right)} \, dx","Int[x^m*(c*Sin[a + b*x^n]^3)^(1/3),x]","\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) \text{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) \text{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) \text{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) \text{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)*E^(I*a)*x^(1 + m)*Csc[a + b*x^n]*Gamma[(1 + m)/n, (-I)*b*x^n]*(c*Sin[a + b*x^n]^3)^(1/3))/(n*((-I)*b*x^n)^((1 + m)/n)) - ((I/2)*x^(1 + m)*Csc[a + b*x^n]*Gamma[(1 + m)/n, I*b*x^n]*(c*Sin[a + b*x^n]^3)^(1/3))/(E^(I*a)*n*(I*b*x^n)^((1 + m)/n))","A",4,3,20,0.1500,1,"{6720, 3423, 2218}"
327,1,143,0,0.2778309,"\int x^3 \sqrt[3]{c \sin ^3\left(a+b x^n\right)} \, dx","Int[x^3*(c*Sin[a + b*x^n]^3)^(1/3),x]","\frac{i e^{i a} x^4 \left(-i b x^n\right)^{-4/n} \text{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} \text{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} \text{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} \text{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)*E^(I*a)*x^4*Csc[a + b*x^n]*Gamma[4/n, (-I)*b*x^n]*(c*Sin[a + b*x^n]^3)^(1/3))/(n*((-I)*b*x^n)^(4/n)) - ((I/2)*x^4*Csc[a + b*x^n]*Gamma[4/n, I*b*x^n]*(c*Sin[a + b*x^n]^3)^(1/3))/(E^(I*a)*n*(I*b*x^n)^(4/n))","A",4,3,20,0.1500,1,"{6720, 3423, 2218}"
328,1,143,0,0.2660284,"\int x^2 \sqrt[3]{c \sin ^3\left(a+b x^n\right)} \, dx","Int[x^2*(c*Sin[a + b*x^n]^3)^(1/3),x]","\frac{i e^{i a} x^3 \left(-i b x^n\right)^{-3/n} \text{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} \text{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} \text{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} \text{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)*E^(I*a)*x^3*Csc[a + b*x^n]*Gamma[3/n, (-I)*b*x^n]*(c*Sin[a + b*x^n]^3)^(1/3))/(n*((-I)*b*x^n)^(3/n)) - ((I/2)*x^3*Csc[a + b*x^n]*Gamma[3/n, I*b*x^n]*(c*Sin[a + b*x^n]^3)^(1/3))/(E^(I*a)*n*(I*b*x^n)^(3/n))","A",4,3,20,0.1500,1,"{6720, 3423, 2218}"
329,1,143,0,0.186104,"\int x \sqrt[3]{c \sin ^3\left(a+b x^n\right)} \, dx","Int[x*(c*Sin[a + b*x^n]^3)^(1/3),x]","\frac{i e^{i a} x^2 \left(-i b x^n\right)^{-2/n} \text{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} \text{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} \text{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} \text{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)*E^(I*a)*x^2*Csc[a + b*x^n]*Gamma[2/n, (-I)*b*x^n]*(c*Sin[a + b*x^n]^3)^(1/3))/(n*((-I)*b*x^n)^(2/n)) - ((I/2)*x^2*Csc[a + b*x^n]*Gamma[2/n, I*b*x^n]*(c*Sin[a + b*x^n]^3)^(1/3))/(E^(I*a)*n*(I*b*x^n)^(2/n))","A",4,3,18,0.1667,1,"{6720, 3423, 2218}"
330,1,135,0,0.0471616,"\int \sqrt[3]{c \sin ^3\left(a+b x^n\right)} \, dx","Int[(c*Sin[a + b*x^n]^3)^(1/3),x]","\frac{i e^{i a} x \left(-i b x^n\right)^{-1/n} \text{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} \text{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} \text{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} \text{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)*E^(I*a)*x*Csc[a + b*x^n]*Gamma[n^(-1), (-I)*b*x^n]*(c*Sin[a + b*x^n]^3)^(1/3))/(n*((-I)*b*x^n)^n^(-1)) - ((I/2)*x*Csc[a + b*x^n]*Gamma[n^(-1), I*b*x^n]*(c*Sin[a + b*x^n]^3)^(1/3))/(E^(I*a)*n*(I*b*x^n)^n^(-1))","A",4,3,16,0.1875,1,"{6720, 3365, 2208}"
331,1,73,0,0.1508655,"\int \frac{\sqrt[3]{c \sin ^3\left(a+b x^n\right)}}{x} \, dx","Int[(c*Sin[a + b*x^n]^3)^(1/3)/x,x]","\frac{\sin (a) \text{CosIntegral}\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}","\frac{\sin (a) \text{CosIntegral}\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,"(CosIntegral[b*x^n]*Csc[a + b*x^n]*Sin[a]*(c*Sin[a + b*x^n]^3)^(1/3))/n + (Cos[a]*Csc[a + b*x^n]*(c*Sin[a + b*x^n]^3)^(1/3)*SinIntegral[b*x^n])/n","A",4,4,20,0.2000,1,"{6720, 3377, 3376, 3375}"
332,1,139,0,0.2045827,"\int \frac{\sqrt[3]{c \sin ^3\left(a+b x^n\right)}}{x^2} \, dx","Int[(c*Sin[a + b*x^n]^3)^(1/3)/x^2,x]","\frac{i e^{i a} \left(-i b x^n\right)^{\frac{1}{n}} \text{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}} \text{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}} \text{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}} \text{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)*E^(I*a)*((-I)*b*x^n)^n^(-1)*Csc[a + b*x^n]*Gamma[-n^(-1), (-I)*b*x^n]*(c*Sin[a + b*x^n]^3)^(1/3))/(n*x) - ((I/2)*(I*b*x^n)^n^(-1)*Csc[a + b*x^n]*Gamma[-n^(-1), I*b*x^n]*(c*Sin[a + b*x^n]^3)^(1/3))/(E^(I*a)*n*x)","A",4,3,20,0.1500,1,"{6720, 3423, 2218}"
333,1,143,0,0.2119503,"\int \frac{\sqrt[3]{c \sin ^3\left(a+b x^n\right)}}{x^3} \, dx","Int[(c*Sin[a + b*x^n]^3)^(1/3)/x^3,x]","\frac{i e^{i a} \left(-i b x^n\right)^{2/n} \text{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} \text{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} \text{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} \text{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)*E^(I*a)*((-I)*b*x^n)^(2/n)*Csc[a + b*x^n]*Gamma[-2/n, (-I)*b*x^n]*(c*Sin[a + b*x^n]^3)^(1/3))/(n*x^2) - ((I/2)*(I*b*x^n)^(2/n)*Csc[a + b*x^n]*Gamma[-2/n, I*b*x^n]*(c*Sin[a + b*x^n]^3)^(1/3))/(E^(I*a)*n*x^2)","A",4,3,20,0.1500,1,"{6720, 3423, 2218}"
334,1,169,0,0.3010688,"\int x^m \left(c \sin ^3(a+b x)\right)^{2/3} \, dx","Int[x^m*(c*Sin[a + b*x]^3)^(2/3),x]","\frac{i e^{2 i a} 2^{-m-3} x^m (-i b x)^{-m} \csc ^2(a+b x) \text{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) \text{Gamma}(m+1,2 i b x) \left(c \sin ^3(a+b x)\right)^{2/3}}{b}+\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) \text{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) \text{Gamma}(m+1,2 i b x) \left(c \sin ^3(a+b x)\right)^{2/3}}{b}+\frac{x^{m+1} \csc ^2(a+b x) \left(c \sin ^3(a+b x)\right)^{2/3}}{2 (m+1)}",1,"(x^(1 + m)*Csc[a + b*x]^2*(c*Sin[a + b*x]^3)^(2/3))/(2*(1 + m)) + (I*2^(-3 - m)*E^((2*I)*a)*x^m*Csc[a + b*x]^2*Gamma[1 + m, (-2*I)*b*x]*(c*Sin[a + b*x]^3)^(2/3))/(b*((-I)*b*x)^m) - (I*2^(-3 - m)*x^m*Csc[a + b*x]^2*Gamma[1 + m, (2*I)*b*x]*(c*Sin[a + b*x]^3)^(2/3))/(b*E^((2*I)*a)*(I*b*x)^m)","A",6,4,18,0.2222,1,"{6720, 3312, 3307, 2181}"
335,1,165,0,0.1881013,"\int x^3 \left(c \sin ^3(a+b x)\right)^{2/3} \, dx","Int[x^3*(c*Sin[a + b*x]^3)^(2/3),x]","\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{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{x^3 \cot (a+b x) \left(c \sin ^3(a+b x)\right)^{2/3}}{2 b}+\frac{1}{8} x^4 \csc ^2(a+b x) \left(c \sin ^3(a+b x)\right)^{2/3}","\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{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{x^3 \cot (a+b x) \left(c \sin ^3(a+b x)\right)^{2/3}}{2 b}+\frac{1}{8} x^4 \csc ^2(a+b x) \left(c \sin ^3(a+b x)\right)^{2/3}",1,"(-3*(c*Sin[a + b*x]^3)^(2/3))/(8*b^4) + (3*x^2*(c*Sin[a + b*x]^3)^(2/3))/(4*b^2) + (3*x*Cot[a + b*x]*(c*Sin[a + b*x]^3)^(2/3))/(4*b^3) - (x^3*Cot[a + b*x]*(c*Sin[a + b*x]^3)^(2/3))/(2*b) - (3*x^2*Csc[a + b*x]^2*(c*Sin[a + b*x]^3)^(2/3))/(8*b^2) + (x^4*Csc[a + b*x]^2*(c*Sin[a + b*x]^3)^(2/3))/8","A",5,4,18,0.2222,1,"{6720, 3311, 30, 3310}"
336,1,139,0,0.1638576,"\int x^2 \left(c \sin ^3(a+b x)\right)^{2/3} \, dx","Int[x^2*(c*Sin[a + b*x]^3)^(2/3),x]","\frac{x \left(c \sin ^3(a+b x)\right)^{2/3}}{2 b^2}+\frac{\cot (a+b x) \left(c \sin ^3(a+b x)\right)^{2/3}}{4 b^3}-\frac{x \csc ^2(a+b x) \left(c \sin ^3(a+b x)\right)^{2/3}}{4 b^2}-\frac{x^2 \cot (a+b x) \left(c \sin ^3(a+b x)\right)^{2/3}}{2 b}+\frac{1}{6} x^3 \csc ^2(a+b x) \left(c \sin ^3(a+b x)\right)^{2/3}","\frac{x \left(c \sin ^3(a+b x)\right)^{2/3}}{2 b^2}+\frac{\cot (a+b x) \left(c \sin ^3(a+b x)\right)^{2/3}}{4 b^3}-\frac{x \csc ^2(a+b x) \left(c \sin ^3(a+b x)\right)^{2/3}}{4 b^2}-\frac{x^2 \cot (a+b x) \left(c \sin ^3(a+b x)\right)^{2/3}}{2 b}+\frac{1}{6} x^3 \csc ^2(a+b x) \left(c \sin ^3(a+b x)\right)^{2/3}",1,"(x*(c*Sin[a + b*x]^3)^(2/3))/(2*b^2) + (Cot[a + b*x]*(c*Sin[a + b*x]^3)^(2/3))/(4*b^3) - (x^2*Cot[a + b*x]*(c*Sin[a + b*x]^3)^(2/3))/(2*b) - (x*Csc[a + b*x]^2*(c*Sin[a + b*x]^3)^(2/3))/(4*b^2) + (x^3*Csc[a + b*x]^2*(c*Sin[a + b*x]^3)^(2/3))/6","A",5,5,18,0.2778,1,"{6720, 3311, 30, 2635, 8}"
337,1,79,0,0.1024832,"\int x \left(c \sin ^3(a+b x)\right)^{2/3} \, dx","Int[x*(c*Sin[a + b*x]^3)^(2/3),x]","\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}","\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,"(c*Sin[a + b*x]^3)^(2/3)/(4*b^2) - (x*Cot[a + b*x]*(c*Sin[a + b*x]^3)^(2/3))/(2*b) + (x^2*Csc[a + b*x]^2*(c*Sin[a + b*x]^3)^(2/3))/4","A",3,3,16,0.1875,1,"{6720, 3310, 30}"
338,1,55,0,0.023013,"\int \left(c \sin ^3(a+b x)\right)^{2/3} \, dx","Int[(c*Sin[a + b*x]^3)^(2/3),x]","\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}","\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,"-(Cot[a + b*x]*(c*Sin[a + b*x]^3)^(2/3))/(2*b) + (x*Csc[a + b*x]^2*(c*Sin[a + b*x]^3)^(2/3))/2","A",3,3,14,0.2143,1,"{3207, 2635, 8}"
339,1,99,0,0.2087332,"\int \frac{\left(c \sin ^3(a+b x)\right)^{2/3}}{x} \, dx","Int[(c*Sin[a + b*x]^3)^(2/3)/x,x]","-\frac{1}{2} \cos (2 a) \text{CosIntegral}(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}","-\frac{1}{2} \cos (2 a) \text{CosIntegral}(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,"-(Cos[2*a]*CosIntegral[2*b*x]*Csc[a + b*x]^2*(c*Sin[a + b*x]^3)^(2/3))/2 + (Csc[a + b*x]^2*Log[x]*(c*Sin[a + b*x]^3)^(2/3))/2 + (Csc[a + b*x]^2*Sin[2*a]*(c*Sin[a + b*x]^3)^(2/3)*SinIntegral[2*b*x])/2","A",6,5,18,0.2778,1,"{6720, 3312, 3303, 3299, 3302}"
340,1,86,0,0.1839082,"\int \frac{\left(c \sin ^3(a+b x)\right)^{2/3}}{x^2} \, dx","Int[(c*Sin[a + b*x]^3)^(2/3)/x^2,x]","b \sin (2 a) \text{CosIntegral}(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}","b \sin (2 a) \text{CosIntegral}(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,"-((c*Sin[a + b*x]^3)^(2/3)/x) + b*CosIntegral[2*b*x]*Csc[a + b*x]^2*Sin[2*a]*(c*Sin[a + b*x]^3)^(2/3) + b*Cos[2*a]*Csc[a + b*x]^2*(c*Sin[a + b*x]^3)^(2/3)*SinIntegral[2*b*x]","A",6,6,18,0.3333,1,"{6720, 3313, 12, 3303, 3299, 3302}"
341,1,119,0,0.2300945,"\int \frac{\left(c \sin ^3(a+b x)\right)^{2/3}}{x^3} \, dx","Int[(c*Sin[a + b*x]^3)^(2/3)/x^3,x]","b^2 \cos (2 a) \text{CosIntegral}(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}","b^2 \cos (2 a) \text{CosIntegral}(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,"-(c*Sin[a + b*x]^3)^(2/3)/(2*x^2) - (b*Cot[a + b*x]*(c*Sin[a + b*x]^3)^(2/3))/x + b^2*Cos[2*a]*CosIntegral[2*b*x]*Csc[a + b*x]^2*(c*Sin[a + b*x]^3)^(2/3) - b^2*Csc[a + b*x]^2*Sin[2*a]*(c*Sin[a + b*x]^3)^(2/3)*SinIntegral[2*b*x]","A",8,7,18,0.3889,1,"{6720, 3314, 29, 3312, 3303, 3299, 3302}"
342,1,209,0,0.2770512,"\int x^m \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3} \, dx","Int[x^m*(c*Sin[a + b*x^2]^3)^(2/3),x]","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) \text{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) \text{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}+\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) \text{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) \text{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}+\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)}",1,"(x^(1 + m)*Csc[a + b*x^2]^2*(c*Sin[a + b*x^2]^3)^(2/3))/(2*(1 + m)) + 2^(-7/2 - m/2)*E^((2*I)*a)*x^(1 + m)*((-I)*b*x^2)^((-1 - m)/2)*Csc[a + b*x^2]^2*Gamma[(1 + m)/2, (-2*I)*b*x^2]*(c*Sin[a + b*x^2]^3)^(2/3) + (2^(-7/2 - m/2)*x^(1 + m)*(I*b*x^2)^((-1 - m)/2)*Csc[a + b*x^2]^2*Gamma[(1 + m)/2, (2*I)*b*x^2]*(c*Sin[a + b*x^2]^3)^(2/3))/E^((2*I)*a)","A",6,4,20,0.2000,1,"{6720, 3403, 3390, 2218}"
343,1,91,0,0.1834934,"\int x^3 \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3} \, dx","Int[x^3*(c*Sin[a + b*x^2]^3)^(2/3),x]","\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}","\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,"(c*Sin[a + b*x^2]^3)^(2/3)/(8*b^2) - (x^2*Cot[a + b*x^2]*(c*Sin[a + b*x^2]^3)^(2/3))/(4*b) + (x^4*Csc[a + b*x^2]^2*(c*Sin[a + b*x^2]^3)^(2/3))/8","A",4,4,20,0.2000,1,"{6720, 3379, 3310, 30}"
344,1,195,0,0.2308884,"\int x^2 \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3} \, dx","Int[x^2*(c*Sin[a + b*x^2]^3)^(2/3),x]","\frac{\sqrt{\pi } \sin (2 a) \text{FresnelC}\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{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}-\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{\sqrt{\pi } \sin (2 a) \text{FresnelC}\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{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}-\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}",1,"(x^3*Csc[a + b*x^2]^2*(c*Sin[a + b*x^2]^3)^(2/3))/6 + (Sqrt[Pi]*Cos[2*a]*Csc[a + b*x^2]^2*FresnelS[(2*Sqrt[b]*x)/Sqrt[Pi]]*(c*Sin[a + b*x^2]^3)^(2/3))/(16*b^(3/2)) + (Sqrt[Pi]*Csc[a + b*x^2]^2*FresnelC[(2*Sqrt[b]*x)/Sqrt[Pi]]*Sin[2*a]*(c*Sin[a + b*x^2]^3)^(2/3))/(16*b^(3/2)) - (x*Csc[a + b*x^2]^2*(c*Sin[a + b*x^2]^3)^(2/3)*Sin[2*a + 2*b*x^2])/(8*b)","A",7,6,20,0.3000,1,"{6720, 3403, 3386, 3353, 3352, 3351}"
345,1,65,0,0.0997761,"\int x \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3} \, dx","Int[x*(c*Sin[a + b*x^2]^3)^(2/3),x]","\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}","\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,"-(Cot[a + b*x^2]*(c*Sin[a + b*x^2]^3)^(2/3))/(4*b) + (x^2*Csc[a + b*x^2]^2*(c*Sin[a + b*x^2]^3)^(2/3))/4","A",4,4,18,0.2222,1,"{6715, 3207, 2635, 8}"
346,1,148,0,0.0583402,"\int \left(c \sin ^3\left(a+b x^2\right)\right)^{2/3} \, dx","Int[(c*Sin[a + b*x^2]^3)^(2/3),x]","-\frac{\sqrt{\pi } \cos (2 a) \text{FresnelC}\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}","-\frac{\sqrt{\pi } \cos (2 a) \text{FresnelC}\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,"(x*Csc[a + b*x^2]^2*(c*Sin[a + b*x^2]^3)^(2/3))/2 - (Sqrt[Pi]*Cos[2*a]*Csc[a + b*x^2]^2*FresnelC[(2*Sqrt[b]*x)/Sqrt[Pi]]*(c*Sin[a + b*x^2]^3)^(2/3))/(4*Sqrt[b]) + (Sqrt[Pi]*Csc[a + b*x^2]^2*FresnelS[(2*Sqrt[b]*x)/Sqrt[Pi]]*Sin[2*a]*(c*Sin[a + b*x^2]^3)^(2/3))/(4*Sqrt[b])","A",6,5,16,0.3125,1,"{6720, 3357, 3354, 3352, 3351}"
347,1,115,0,0.1332114,"\int \frac{\left(c \sin ^3\left(a+b x^2\right)\right)^{2/3}}{x} \, dx","Int[(c*Sin[a + b*x^2]^3)^(2/3)/x,x]","-\frac{1}{4} \cos (2 a) \text{CosIntegral}\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}","-\frac{1}{4} \cos (2 a) \text{CosIntegral}\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,"-(Cos[2*a]*CosIntegral[2*b*x^2]*Csc[a + b*x^2]^2*(c*Sin[a + b*x^2]^3)^(2/3))/4 + (Csc[a + b*x^2]^2*Log[x]*(c*Sin[a + b*x^2]^3)^(2/3))/2 + (Csc[a + b*x^2]^2*Sin[2*a]*(c*Sin[a + b*x^2]^3)^(2/3)*SinIntegral[2*b*x^2])/4","A",6,5,20,0.2500,1,"{6720, 3403, 3378, 3376, 3375}"
348,1,132,0,0.1483208,"\int \frac{\left(c \sin ^3\left(a+b x^2\right)\right)^{2/3}}{x^2} \, dx","Int[(c*Sin[a + b*x^2]^3)^(2/3)/x^2,x]","\sqrt{\pi } \sqrt{b} \sin (2 a) \text{FresnelC}\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}","\sqrt{\pi } \sqrt{b} \sin (2 a) \text{FresnelC}\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,"-((c*Sin[a + b*x^2]^3)^(2/3)/x) + Sqrt[b]*Sqrt[Pi]*Cos[2*a]*Csc[a + b*x^2]^2*FresnelS[(2*Sqrt[b]*x)/Sqrt[Pi]]*(c*Sin[a + b*x^2]^3)^(2/3) + Sqrt[b]*Sqrt[Pi]*Csc[a + b*x^2]^2*FresnelC[(2*Sqrt[b]*x)/Sqrt[Pi]]*Sin[2*a]*(c*Sin[a + b*x^2]^3)^(2/3)","A",7,7,20,0.3500,1,"{6720, 3393, 4573, 3373, 3353, 3352, 3351}"
349,1,161,0,0.2149489,"\int \frac{\left(c \sin ^3\left(a+b x^2\right)\right)^{2/3}}{x^3} \, dx","Int[(c*Sin[a + b*x^2]^3)^(2/3)/x^3,x]","\frac{1}{2} b \sin (2 a) \text{CosIntegral}\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}","\frac{1}{2} b \sin (2 a) \text{CosIntegral}\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))/(4*x^2) + (Cos[2*(a + b*x^2)]*Csc[a + b*x^2]^2*(c*Sin[a + b*x^2]^3)^(2/3))/(4*x^2) + (b*CosIntegral[2*b*x^2]*Csc[a + b*x^2]^2*Sin[2*a]*(c*Sin[a + b*x^2]^3)^(2/3))/2 + (b*Cos[2*a]*Csc[a + b*x^2]^2*(c*Sin[a + b*x^2]^3)^(2/3)*SinIntegral[2*b*x^2])/2","A",8,7,20,0.3500,1,"{6720, 3403, 3380, 3297, 3303, 3299, 3302}"
350,1,217,0,0.364997,"\int x^m \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3} \, dx","Int[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(-i b x^n\right)^{-\frac{m+1}{n}} \csc ^2\left(a+b x^n\right) \text{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) \text{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{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) \text{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) \text{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{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)}",1,"(x^(1 + m)*Csc[a + b*x^n]^2*(c*Sin[a + b*x^n]^3)^(2/3))/(2*(1 + m)) + (E^((2*I)*a)*x^(1 + m)*Csc[a + b*x^n]^2*Gamma[(1 + m)/n, (-2*I)*b*x^n]*(c*Sin[a + b*x^n]^3)^(2/3))/(2^((1 + m + 2*n)/n)*n*((-I)*b*x^n)^((1 + m)/n)) + (x^(1 + m)*Csc[a + b*x^n]^2*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)*n*(I*b*x^n)^((1 + m)/n))","A",6,4,20,0.2000,1,"{6720, 3425, 3424, 2218}"
351,1,188,0,0.3412627,"\int x^3 \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3} \, dx","Int[x^3*(c*Sin[a + b*x^n]^3)^(2/3),x]","\frac{e^{2 i a} 4^{-\frac{2}{n}-1} x^4 \left(-i b x^n\right)^{-4/n} \text{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} \text{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{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} \text{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} \text{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{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}",1,"(x^4*Csc[a + b*x^n]^2*(c*Sin[a + b*x^n]^3)^(2/3))/8 + (4^(-1 - 2/n)*E^((2*I)*a)*x^4*Csc[a + b*x^n]^2*Gamma[4/n, (-2*I)*b*x^n]*(c*Sin[a + b*x^n]^3)^(2/3))/(n*((-I)*b*x^n)^(4/n)) + (4^(-1 - 2/n)*x^4*Csc[a + b*x^n]^2*Gamma[4/n, (2*I)*b*x^n]*(c*Sin[a + b*x^n]^3)^(2/3))/(E^((2*I)*a)*n*(I*b*x^n)^(4/n))","A",6,4,20,0.2000,1,"{6720, 3425, 3424, 2218}"
352,1,188,0,0.3145486,"\int x^2 \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3} \, dx","Int[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(-i b x^n\right)^{-3/n} \text{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} \text{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{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} \text{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} \text{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{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}",1,"(x^3*Csc[a + b*x^n]^2*(c*Sin[a + b*x^n]^3)^(2/3))/6 + (2^(-2 - 3/n)*E^((2*I)*a)*x^3*Csc[a + b*x^n]^2*Gamma[3/n, (-2*I)*b*x^n]*(c*Sin[a + b*x^n]^3)^(2/3))/(n*((-I)*b*x^n)^(3/n)) + (2^(-2 - 3/n)*x^3*Csc[a + b*x^n]^2*Gamma[3/n, (2*I)*b*x^n]*(c*Sin[a + b*x^n]^3)^(2/3))/(E^((2*I)*a)*n*(I*b*x^n)^(3/n))","A",6,4,20,0.2000,1,"{6720, 3425, 3424, 2218}"
353,1,188,0,0.2404306,"\int x \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3} \, dx","Int[x*(c*Sin[a + b*x^n]^3)^(2/3),x]","\frac{e^{2 i a} 4^{-\frac{1}{n}-1} x^2 \left(-i b x^n\right)^{-2/n} \text{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} \text{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{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} \text{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} \text{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{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}",1,"(x^2*Csc[a + b*x^n]^2*(c*Sin[a + b*x^n]^3)^(2/3))/4 + (4^(-1 - n^(-1))*E^((2*I)*a)*x^2*Csc[a + b*x^n]^2*Gamma[2/n, (-2*I)*b*x^n]*(c*Sin[a + b*x^n]^3)^(2/3))/(n*((-I)*b*x^n)^(2/n)) + (4^(-1 - n^(-1))*x^2*Csc[a + b*x^n]^2*Gamma[2/n, (2*I)*b*x^n]*(c*Sin[a + b*x^n]^3)^(2/3))/(E^((2*I)*a)*n*(I*b*x^n)^(2/n))","A",6,4,18,0.2222,1,"{6720, 3425, 3424, 2218}"
354,1,178,0,0.0888038,"\int \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3} \, dx","Int[(c*Sin[a + b*x^n]^3)^(2/3),x]","\frac{e^{2 i a} 2^{-\frac{1}{n}-2} x \left(-i b x^n\right)^{-1/n} \text{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} \text{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{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} \text{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} \text{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{1}{2} x \csc ^2\left(a+b x^n\right) \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}",1,"(x*Csc[a + b*x^n]^2*(c*Sin[a + b*x^n]^3)^(2/3))/2 + (2^(-2 - n^(-1))*E^((2*I)*a)*x*Csc[a + b*x^n]^2*Gamma[n^(-1), (-2*I)*b*x^n]*(c*Sin[a + b*x^n]^3)^(2/3))/(n*((-I)*b*x^n)^n^(-1)) + (2^(-2 - n^(-1))*x*Csc[a + b*x^n]^2*Gamma[n^(-1), (2*I)*b*x^n]*(c*Sin[a + b*x^n]^3)^(2/3))/(E^((2*I)*a)*n*(I*b*x^n)^n^(-1))","A",6,4,16,0.2500,1,"{6720, 3367, 3366, 2208}"
355,1,121,0,0.1789813,"\int \frac{\left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}}{x} \, dx","Int[(c*Sin[a + b*x^n]^3)^(2/3)/x,x]","-\frac{\cos (2 a) \text{CosIntegral}\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}","-\frac{\cos (2 a) \text{CosIntegral}\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,"-(Cos[2*a]*CosIntegral[2*b*x^n]*Csc[a + b*x^n]^2*(c*Sin[a + b*x^n]^3)^(2/3))/(2*n) + (Csc[a + b*x^n]^2*Log[x]*(c*Sin[a + b*x^n]^3)^(2/3))/2 + (Csc[a + b*x^n]^2*Sin[2*a]*(c*Sin[a + b*x^n]^3)^(2/3)*SinIntegral[2*b*x^n])/(2*n)","A",6,5,20,0.2500,1,"{6720, 3425, 3378, 3376, 3375}"
356,1,180,0,0.2754356,"\int \frac{\left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}}{x^2} \, dx","Int[(c*Sin[a + b*x^n]^3)^(2/3)/x^2,x]","\frac{e^{2 i a} 2^{\frac{1}{n}-2} \left(-i b x^n\right)^{\frac{1}{n}} \text{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}} \text{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{\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}} \text{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}} \text{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{\csc ^2\left(a+b x^n\right) \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}}{2 x}",1,"-(Csc[a + b*x^n]^2*(c*Sin[a + b*x^n]^3)^(2/3))/(2*x) + (2^(-2 + n^(-1))*E^((2*I)*a)*((-I)*b*x^n)^n^(-1)*Csc[a + b*x^n]^2*Gamma[-n^(-1), (-2*I)*b*x^n]*(c*Sin[a + b*x^n]^3)^(2/3))/(n*x) + (2^(-2 + n^(-1))*(I*b*x^n)^n^(-1)*Csc[a + b*x^n]^2*Gamma[-n^(-1), (2*I)*b*x^n]*(c*Sin[a + b*x^n]^3)^(2/3))/(E^((2*I)*a)*n*x)","A",6,4,20,0.2000,1,"{6720, 3425, 3424, 2218}"
357,1,184,0,0.2686424,"\int \frac{\left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}}{x^3} \, dx","Int[(c*Sin[a + b*x^n]^3)^(2/3)/x^3,x]","\frac{e^{2 i a} 4^{\frac{1}{n}-1} \left(-i b x^n\right)^{2/n} \text{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} \text{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{\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} \text{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} \text{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{\csc ^2\left(a+b x^n\right) \left(c \sin ^3\left(a+b x^n\right)\right)^{2/3}}{4 x^2}",1,"-(Csc[a + b*x^n]^2*(c*Sin[a + b*x^n]^3)^(2/3))/(4*x^2) + (4^(-1 + n^(-1))*E^((2*I)*a)*((-I)*b*x^n)^(2/n)*Csc[a + b*x^n]^2*Gamma[-2/n, (-2*I)*b*x^n]*(c*Sin[a + b*x^n]^3)^(2/3))/(n*x^2) + (4^(-1 + n^(-1))*(I*b*x^n)^(2/n)*Csc[a + b*x^n]^2*Gamma[-2/n, (2*I)*b*x^n]*(c*Sin[a + b*x^n]^3)^(2/3))/(E^((2*I)*a)*n*x^2)","A",6,4,20,0.2000,1,"{6720, 3425, 3424, 2218}"