1,1,249,0,0.2428307,"\int x^2 \sin \left(a+b x+c x^2\right) \, dx","Int[x^2*Sin[a + b*x + c*x^2],x]","\frac{\sqrt{\frac{\pi }{2}} b^2 \sin \left(a-\frac{b^2}{4 c}\right) \text{FresnelC}\left(\frac{b+2 c x}{\sqrt{2 \pi } \sqrt{c}}\right)}{4 c^{5/2}}+\frac{\sqrt{\frac{\pi }{2}} \cos \left(a-\frac{b^2}{4 c}\right) \text{FresnelC}\left(\frac{b+2 c x}{\sqrt{2 \pi } \sqrt{c}}\right)}{2 c^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} \sin \left(a-\frac{b^2}{4 c}\right) S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)}{2 c^{3/2}}+\frac{\sqrt{\frac{\pi }{2}} b^2 \cos \left(a-\frac{b^2}{4 c}\right) S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)}{4 c^{5/2}}+\frac{b \cos \left(a+b x+c x^2\right)}{4 c^2}-\frac{x \cos \left(a+b x+c x^2\right)}{2 c}","\frac{\sqrt{\frac{\pi }{2}} b^2 \sin \left(a-\frac{b^2}{4 c}\right) \text{FresnelC}\left(\frac{b+2 c x}{\sqrt{2 \pi } \sqrt{c}}\right)}{4 c^{5/2}}+\frac{\sqrt{\frac{\pi }{2}} \cos \left(a-\frac{b^2}{4 c}\right) \text{FresnelC}\left(\frac{b+2 c x}{\sqrt{2 \pi } \sqrt{c}}\right)}{2 c^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} \sin \left(a-\frac{b^2}{4 c}\right) S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)}{2 c^{3/2}}+\frac{\sqrt{\frac{\pi }{2}} b^2 \cos \left(a-\frac{b^2}{4 c}\right) S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)}{4 c^{5/2}}+\frac{b \cos \left(a+b x+c x^2\right)}{4 c^2}-\frac{x \cos \left(a+b x+c x^2\right)}{2 c}",1,"(b*Cos[a + b*x + c*x^2])/(4*c^2) - (x*Cos[a + b*x + c*x^2])/(2*c) + (Sqrt[Pi/2]*Cos[a - b^2/(4*c)]*FresnelC[(b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])])/(2*c^(3/2)) + (b^2*Sqrt[Pi/2]*Cos[a - b^2/(4*c)]*FresnelS[(b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])])/(4*c^(5/2)) + (b^2*Sqrt[Pi/2]*FresnelC[(b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])]*Sin[a - b^2/(4*c)])/(4*c^(5/2)) - (Sqrt[Pi/2]*FresnelS[(b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])]*Sin[a - b^2/(4*c)])/(2*c^(3/2))","A",8,6,15,0.4000,1,"{3463, 3448, 3352, 3351, 3461, 3447}"
2,1,123,0,0.0371549,"\int x \sin \left(a+b x+c x^2\right) \, dx","Int[x*Sin[a + b*x + c*x^2],x]","-\frac{\sqrt{\frac{\pi }{2}} b \sin \left(a-\frac{b^2}{4 c}\right) \text{FresnelC}\left(\frac{b+2 c x}{\sqrt{2 \pi } \sqrt{c}}\right)}{2 c^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} b \cos \left(a-\frac{b^2}{4 c}\right) S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)}{2 c^{3/2}}-\frac{\cos \left(a+b x+c x^2\right)}{2 c}","-\frac{\sqrt{\frac{\pi }{2}} b \sin \left(a-\frac{b^2}{4 c}\right) \text{FresnelC}\left(\frac{b+2 c x}{\sqrt{2 \pi } \sqrt{c}}\right)}{2 c^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} b \cos \left(a-\frac{b^2}{4 c}\right) S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)}{2 c^{3/2}}-\frac{\cos \left(a+b x+c x^2\right)}{2 c}",1,"-Cos[a + b*x + c*x^2]/(2*c) - (b*Sqrt[Pi/2]*Cos[a - b^2/(4*c)]*FresnelS[(b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])])/(2*c^(3/2)) - (b*Sqrt[Pi/2]*FresnelC[(b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])]*Sin[a - b^2/(4*c)])/(2*c^(3/2))","A",4,4,13,0.3077,1,"{3461, 3447, 3351, 3352}"
3,1,97,0,0.0212291,"\int \sin \left(a+b x+c x^2\right) \, dx","Int[Sin[a + b*x + c*x^2],x]","\frac{\sqrt{\frac{\pi }{2}} \sin \left(a-\frac{b^2}{4 c}\right) \text{FresnelC}\left(\frac{b+2 c x}{\sqrt{2 \pi } \sqrt{c}}\right)}{\sqrt{c}}+\frac{\sqrt{\frac{\pi }{2}} \cos \left(a-\frac{b^2}{4 c}\right) S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)}{\sqrt{c}}","\frac{\sqrt{\frac{\pi }{2}} \sin \left(a-\frac{b^2}{4 c}\right) \text{FresnelC}\left(\frac{b+2 c x}{\sqrt{2 \pi } \sqrt{c}}\right)}{\sqrt{c}}+\frac{\sqrt{\frac{\pi }{2}} \cos \left(a-\frac{b^2}{4 c}\right) S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)}{\sqrt{c}}",1,"(Sqrt[Pi/2]*Cos[a - b^2/(4*c)]*FresnelS[(b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])])/Sqrt[c] + (Sqrt[Pi/2]*FresnelC[(b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])]*Sin[a - b^2/(4*c)])/Sqrt[c]","A",3,3,11,0.2727,1,"{3447, 3351, 3352}"
4,0,0,0,0.0082178,"\int \frac{\sin \left(a+b x+c x^2\right)}{x} \, dx","Int[Sin[a + b*x + c*x^2]/x,x]","\int \frac{\sin \left(a+b x+c x^2\right)}{x} \, dx","\text{Int}\left(\frac{\sin \left(a+b x+c x^2\right)}{x},x\right)",0,"Defer[Int][Sin[a + b*x + c*x^2]/x, x]","A",0,0,0,0,-1,"{}"
5,1,110,0,0.0831945,"\int \left(-\frac{b \cos \left(a+b x+c x^2\right)}{x}+\frac{\sin \left(a+b x+c x^2\right)}{x^2}\right) \, dx","Int[-((b*Cos[a + b*x + c*x^2])/x) + Sin[a + b*x + c*x^2]/x^2,x]","\sqrt{2 \pi } \sqrt{c} \cos \left(a-\frac{b^2}{4 c}\right) \text{FresnelC}\left(\frac{b+2 c x}{\sqrt{2 \pi } \sqrt{c}}\right)-\sqrt{2 \pi } \sqrt{c} \sin \left(a-\frac{b^2}{4 c}\right) S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)-\frac{\sin \left(a+b x+c x^2\right)}{x}","\sqrt{2 \pi } \sqrt{c} \cos \left(a-\frac{b^2}{4 c}\right) \text{FresnelC}\left(\frac{b+2 c x}{\sqrt{2 \pi } \sqrt{c}}\right)-\sqrt{2 \pi } \sqrt{c} \sin \left(a-\frac{b^2}{4 c}\right) S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)-\frac{\sin \left(a+b x+c x^2\right)}{x}",1,"Sqrt[c]*Sqrt[2*Pi]*Cos[a - b^2/(4*c)]*FresnelC[(b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])] - Sqrt[c]*Sqrt[2*Pi]*FresnelS[(b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])]*Sin[a - b^2/(4*c)] - Sin[a + b*x + c*x^2]/x","A",5,4,33,0.1212,1,"{3465, 3448, 3352, 3351}"
6,1,251,0,0.2038839,"\int x^2 \sin \left(a+b x-c x^2\right) \, dx","Int[x^2*Sin[a + b*x - c*x^2],x]","-\frac{\sqrt{\frac{\pi }{2}} b^2 \sin \left(a+\frac{b^2}{4 c}\right) \text{FresnelC}\left(\frac{b-2 c x}{\sqrt{2 \pi } \sqrt{c}}\right)}{4 c^{5/2}}+\frac{\sqrt{\frac{\pi }{2}} \cos \left(a+\frac{b^2}{4 c}\right) \text{FresnelC}\left(\frac{b-2 c x}{\sqrt{2 \pi } \sqrt{c}}\right)}{2 c^{3/2}}+\frac{\sqrt{\frac{\pi }{2}} \sin \left(a+\frac{b^2}{4 c}\right) S\left(\frac{b-2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)}{2 c^{3/2}}+\frac{\sqrt{\frac{\pi }{2}} b^2 \cos \left(a+\frac{b^2}{4 c}\right) S\left(\frac{b-2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)}{4 c^{5/2}}+\frac{b \cos \left(a+b x-c x^2\right)}{4 c^2}+\frac{x \cos \left(a+b x-c x^2\right)}{2 c}","-\frac{\sqrt{\frac{\pi }{2}} b^2 \sin \left(a+\frac{b^2}{4 c}\right) \text{FresnelC}\left(\frac{b-2 c x}{\sqrt{2 \pi } \sqrt{c}}\right)}{4 c^{5/2}}+\frac{\sqrt{\frac{\pi }{2}} \cos \left(a+\frac{b^2}{4 c}\right) \text{FresnelC}\left(\frac{b-2 c x}{\sqrt{2 \pi } \sqrt{c}}\right)}{2 c^{3/2}}+\frac{\sqrt{\frac{\pi }{2}} \sin \left(a+\frac{b^2}{4 c}\right) S\left(\frac{b-2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)}{2 c^{3/2}}+\frac{\sqrt{\frac{\pi }{2}} b^2 \cos \left(a+\frac{b^2}{4 c}\right) S\left(\frac{b-2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)}{4 c^{5/2}}+\frac{b \cos \left(a+b x-c x^2\right)}{4 c^2}+\frac{x \cos \left(a+b x-c x^2\right)}{2 c}",1,"(b*Cos[a + b*x - c*x^2])/(4*c^2) + (x*Cos[a + b*x - c*x^2])/(2*c) + (Sqrt[Pi/2]*Cos[a + b^2/(4*c)]*FresnelC[(b - 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])])/(2*c^(3/2)) + (b^2*Sqrt[Pi/2]*Cos[a + b^2/(4*c)]*FresnelS[(b - 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])])/(4*c^(5/2)) - (b^2*Sqrt[Pi/2]*FresnelC[(b - 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])]*Sin[a + b^2/(4*c)])/(4*c^(5/2)) + (Sqrt[Pi/2]*FresnelS[(b - 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])]*Sin[a + b^2/(4*c)])/(2*c^(3/2))","A",8,6,16,0.3750,1,"{3463, 3448, 3352, 3351, 3461, 3447}"
7,1,124,0,0.0444542,"\int x \sin \left(a+b x-c x^2\right) \, dx","Int[x*Sin[a + b*x - c*x^2],x]","-\frac{\sqrt{\frac{\pi }{2}} b \sin \left(a+\frac{b^2}{4 c}\right) \text{FresnelC}\left(\frac{b-2 c x}{\sqrt{2 \pi } \sqrt{c}}\right)}{2 c^{3/2}}+\frac{\sqrt{\frac{\pi }{2}} b \cos \left(a+\frac{b^2}{4 c}\right) S\left(\frac{b-2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)}{2 c^{3/2}}+\frac{\cos \left(a+b x-c x^2\right)}{2 c}","-\frac{\sqrt{\frac{\pi }{2}} b \sin \left(a+\frac{b^2}{4 c}\right) \text{FresnelC}\left(\frac{b-2 c x}{\sqrt{2 \pi } \sqrt{c}}\right)}{2 c^{3/2}}+\frac{\sqrt{\frac{\pi }{2}} b \cos \left(a+\frac{b^2}{4 c}\right) S\left(\frac{b-2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)}{2 c^{3/2}}+\frac{\cos \left(a+b x-c x^2\right)}{2 c}",1,"Cos[a + b*x - c*x^2]/(2*c) + (b*Sqrt[Pi/2]*Cos[a + b^2/(4*c)]*FresnelS[(b - 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])])/(2*c^(3/2)) - (b*Sqrt[Pi/2]*FresnelC[(b - 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])]*Sin[a + b^2/(4*c)])/(2*c^(3/2))","A",4,4,14,0.2857,1,"{3461, 3447, 3351, 3352}"
8,1,98,0,0.0248944,"\int \sin \left(a+b x-c x^2\right) \, dx","Int[Sin[a + b*x - c*x^2],x]","\frac{\sqrt{\frac{\pi }{2}} \cos \left(a+\frac{b^2}{4 c}\right) S\left(\frac{b-2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)}{\sqrt{c}}-\frac{\sqrt{\frac{\pi }{2}} \sin \left(a+\frac{b^2}{4 c}\right) \text{FresnelC}\left(\frac{b-2 c x}{\sqrt{2 \pi } \sqrt{c}}\right)}{\sqrt{c}}","\frac{\sqrt{\frac{\pi }{2}} \cos \left(a+\frac{b^2}{4 c}\right) S\left(\frac{b-2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)}{\sqrt{c}}-\frac{\sqrt{\frac{\pi }{2}} \sin \left(a+\frac{b^2}{4 c}\right) \text{FresnelC}\left(\frac{b-2 c x}{\sqrt{2 \pi } \sqrt{c}}\right)}{\sqrt{c}}",1,"(Sqrt[Pi/2]*Cos[a + b^2/(4*c)]*FresnelS[(b - 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])])/Sqrt[c] - (Sqrt[Pi/2]*FresnelC[(b - 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])]*Sin[a + b^2/(4*c)])/Sqrt[c]","A",3,3,12,0.2500,1,"{3447, 3351, 3352}"
9,0,0,0,0.0081506,"\int \frac{\sin \left(a+b x-c x^2\right)}{x} \, dx","Int[Sin[a + b*x - c*x^2]/x,x]","\int \frac{\sin \left(a+b x-c x^2\right)}{x} \, dx","\text{Int}\left(\frac{\sin \left(a+b x-c x^2\right)}{x},x\right)",0,"Defer[Int][Sin[a + b*x - c*x^2]/x, x]","A",0,0,0,0,-1,"{}"
10,1,110,0,0.084384,"\int \left(-\frac{b \cos \left(a+b x-c x^2\right)}{x}+\frac{\sin \left(a+b x-c x^2\right)}{x^2}\right) \, dx","Int[-((b*Cos[a + b*x - c*x^2])/x) + Sin[a + b*x - c*x^2]/x^2,x]","\sqrt{2 \pi } \sqrt{c} \cos \left(a+\frac{b^2}{4 c}\right) \text{FresnelC}\left(\frac{b-2 c x}{\sqrt{2 \pi } \sqrt{c}}\right)+\sqrt{2 \pi } \sqrt{c} \sin \left(a+\frac{b^2}{4 c}\right) S\left(\frac{b-2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)-\frac{\sin \left(a+b x-c x^2\right)}{x}","\sqrt{2 \pi } \sqrt{c} \cos \left(a+\frac{b^2}{4 c}\right) \text{FresnelC}\left(\frac{b-2 c x}{\sqrt{2 \pi } \sqrt{c}}\right)+\sqrt{2 \pi } \sqrt{c} \sin \left(a+\frac{b^2}{4 c}\right) S\left(\frac{b-2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)-\frac{\sin \left(a+b x-c x^2\right)}{x}",1,"Sqrt[c]*Sqrt[2*Pi]*Cos[a + b^2/(4*c)]*FresnelC[(b - 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])] + Sqrt[c]*Sqrt[2*Pi]*FresnelS[(b - 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])]*Sin[a + b^2/(4*c)] - Sin[a + b*x - c*x^2]/x","A",5,4,35,0.1143,1,"{3465, 3448, 3352, 3351}"
11,1,82,0,0.0330391,"\int x^2 \sin \left(\frac{1}{4}+x+x^2\right) \, dx","Int[x^2*Sin[1/4 + x + x^2],x]","\frac{1}{2} \sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\frac{2 x+1}{\sqrt{2 \pi }}\right)+\frac{1}{4} \sqrt{\frac{\pi }{2}} S\left(\frac{2 x+1}{\sqrt{2 \pi }}\right)-\frac{1}{2} x \cos \left(x^2+x+\frac{1}{4}\right)+\frac{1}{4} \cos \left(x^2+x+\frac{1}{4}\right)","\frac{1}{2} \sqrt{\frac{\pi }{2}} \text{FresnelC}\left(\frac{2 x+1}{\sqrt{2 \pi }}\right)+\frac{1}{4} \sqrt{\frac{\pi }{2}} S\left(\frac{2 x+1}{\sqrt{2 \pi }}\right)-\frac{1}{2} x \cos \left(x^2+x+\frac{1}{4}\right)+\frac{1}{4} \cos \left(x^2+x+\frac{1}{4}\right)",1,"Cos[1/4 + x + x^2]/4 - (x*Cos[1/4 + x + x^2])/2 + (Sqrt[Pi/2]*FresnelC[(1 + 2*x)/Sqrt[2*Pi]])/2 + (Sqrt[Pi/2]*FresnelS[(1 + 2*x)/Sqrt[2*Pi]])/4","A",6,6,13,0.4615,1,"{3463, 3446, 3352, 3461, 3445, 3351}"
12,1,41,0,0.0129375,"\int x \sin \left(\frac{1}{4}+x+x^2\right) \, dx","Int[x*Sin[1/4 + x + x^2],x]","-\frac{1}{2} \sqrt{\frac{\pi }{2}} S\left(\frac{2 x+1}{\sqrt{2 \pi }}\right)-\frac{1}{2} \cos \left(x^2+x+\frac{1}{4}\right)","-\frac{1}{2} \sqrt{\frac{\pi }{2}} S\left(\frac{2 x+1}{\sqrt{2 \pi }}\right)-\frac{1}{2} \cos \left(x^2+x+\frac{1}{4}\right)",1,"-Cos[1/4 + x + x^2]/2 - (Sqrt[Pi/2]*FresnelS[(1 + 2*x)/Sqrt[2*Pi]])/2","A",3,3,11,0.2727,1,"{3461, 3445, 3351}"
13,1,24,0,0.0060308,"\int \sin \left(\frac{1}{4}+x+x^2\right) \, dx","Int[Sin[1/4 + x + x^2],x]","\sqrt{\frac{\pi }{2}} S\left(\frac{2 x+1}{\sqrt{2 \pi }}\right)","\sqrt{\frac{\pi }{2}} S\left(\frac{2 x+1}{\sqrt{2 \pi }}\right)",1,"Sqrt[Pi/2]*FresnelS[(1 + 2*x)/Sqrt[2*Pi]]","A",2,2,9,0.2222,1,"{3445, 3351}"
14,0,0,0,0.0080294,"\int \frac{\sin \left(\frac{1}{4}+x+x^2\right)}{x} \, dx","Int[Sin[1/4 + x + x^2]/x,x]","\int \frac{\sin \left(\frac{1}{4}+x+x^2\right)}{x} \, dx","\text{Int}\left(\frac{\sin \left(x^2+x+\frac{1}{4}\right)}{x},x\right)",0,"Defer[Int][Sin[1/4 + x + x^2]/x, x]","A",0,0,0,0,-1,"{}"
15,0,0,0,0.0246402,"\int \frac{\sin \left(\frac{1}{4}+x+x^2\right)}{x^2} \, dx","Int[Sin[1/4 + x + x^2]/x^2,x]","\int \frac{\sin \left(\frac{1}{4}+x+x^2\right)}{x^2} \, dx","\text{Int}\left(\frac{\cos \left(x^2+x+\frac{1}{4}\right)}{x},x\right)+\sqrt{2 \pi } \text{FresnelC}\left(\frac{2 x+1}{\sqrt{2 \pi }}\right)-\frac{\sin \left(x^2+x+\frac{1}{4}\right)}{x}",0,"Sqrt[2*Pi]*FresnelC[(1 + 2*x)/Sqrt[2*Pi]] - Sin[1/4 + x + x^2]/x + Defer[Int][Cos[1/4 + x + x^2]/x, x]","A",0,0,0,0,-1,"{}"
16,1,248,0,0.2271808,"\int x^2 \sin ^2\left(a+b x+c x^2\right) \, dx","Int[x^2*Sin[a + b*x + c*x^2]^2,x]","\frac{\sqrt{\pi } \sin \left(2 a-\frac{b^2}{2 c}\right) \text{FresnelC}\left(\frac{b+2 c x}{\sqrt{\pi } \sqrt{c}}\right)}{16 c^{3/2}}-\frac{\sqrt{\pi } b^2 \cos \left(2 a-\frac{b^2}{2 c}\right) \text{FresnelC}\left(\frac{b+2 c x}{\sqrt{\pi } \sqrt{c}}\right)}{16 c^{5/2}}+\frac{\sqrt{\pi } b^2 \sin \left(2 a-\frac{b^2}{2 c}\right) S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{\pi }}\right)}{16 c^{5/2}}+\frac{\sqrt{\pi } \cos \left(2 a-\frac{b^2}{2 c}\right) S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{\pi }}\right)}{16 c^{3/2}}+\frac{b \sin \left(2 a+2 b x+2 c x^2\right)}{16 c^2}-\frac{x \sin \left(2 a+2 b x+2 c x^2\right)}{8 c}+\frac{x^3}{6}","\frac{\sqrt{\pi } \sin \left(2 a-\frac{b^2}{2 c}\right) \text{FresnelC}\left(\frac{b+2 c x}{\sqrt{\pi } \sqrt{c}}\right)}{16 c^{3/2}}-\frac{\sqrt{\pi } b^2 \cos \left(2 a-\frac{b^2}{2 c}\right) \text{FresnelC}\left(\frac{b+2 c x}{\sqrt{\pi } \sqrt{c}}\right)}{16 c^{5/2}}+\frac{\sqrt{\pi } b^2 \sin \left(2 a-\frac{b^2}{2 c}\right) S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{\pi }}\right)}{16 c^{5/2}}+\frac{\sqrt{\pi } \cos \left(2 a-\frac{b^2}{2 c}\right) S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{\pi }}\right)}{16 c^{3/2}}+\frac{b \sin \left(2 a+2 b x+2 c x^2\right)}{16 c^2}-\frac{x \sin \left(2 a+2 b x+2 c x^2\right)}{8 c}+\frac{x^3}{6}",1,"x^3/6 - (b^2*Sqrt[Pi]*Cos[2*a - b^2/(2*c)]*FresnelC[(b + 2*c*x)/(Sqrt[c]*Sqrt[Pi])])/(16*c^(5/2)) + (Sqrt[Pi]*Cos[2*a - b^2/(2*c)]*FresnelS[(b + 2*c*x)/(Sqrt[c]*Sqrt[Pi])])/(16*c^(3/2)) + (Sqrt[Pi]*FresnelC[(b + 2*c*x)/(Sqrt[c]*Sqrt[Pi])]*Sin[2*a - b^2/(2*c)])/(16*c^(3/2)) + (b^2*Sqrt[Pi]*FresnelS[(b + 2*c*x)/(Sqrt[c]*Sqrt[Pi])]*Sin[2*a - b^2/(2*c)])/(16*c^(5/2)) + (b*Sin[2*a + 2*b*x + 2*c*x^2])/(16*c^2) - (x*Sin[2*a + 2*b*x + 2*c*x^2])/(8*c)","A",10,7,17,0.4118,1,"{3467, 3464, 3447, 3351, 3352, 3462, 3448}"
17,1,126,0,0.0728105,"\int x \sin ^2\left(a+b x+c x^2\right) \, dx","Int[x*Sin[a + b*x + c*x^2]^2,x]","\frac{\sqrt{\pi } b \cos \left(2 a-\frac{b^2}{2 c}\right) \text{FresnelC}\left(\frac{b+2 c x}{\sqrt{\pi } \sqrt{c}}\right)}{8 c^{3/2}}-\frac{\sqrt{\pi } b \sin \left(2 a-\frac{b^2}{2 c}\right) S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{\pi }}\right)}{8 c^{3/2}}-\frac{\sin \left(2 a+2 b x+2 c x^2\right)}{8 c}+\frac{x^2}{4}","\frac{\sqrt{\pi } b \cos \left(2 a-\frac{b^2}{2 c}\right) \text{FresnelC}\left(\frac{b+2 c x}{\sqrt{\pi } \sqrt{c}}\right)}{8 c^{3/2}}-\frac{\sqrt{\pi } b \sin \left(2 a-\frac{b^2}{2 c}\right) S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{\pi }}\right)}{8 c^{3/2}}-\frac{\sin \left(2 a+2 b x+2 c x^2\right)}{8 c}+\frac{x^2}{4}",1,"x^2/4 + (b*Sqrt[Pi]*Cos[2*a - b^2/(2*c)]*FresnelC[(b + 2*c*x)/(Sqrt[c]*Sqrt[Pi])])/(8*c^(3/2)) - (b*Sqrt[Pi]*FresnelS[(b + 2*c*x)/(Sqrt[c]*Sqrt[Pi])]*Sin[2*a - b^2/(2*c)])/(8*c^(3/2)) - Sin[2*a + 2*b*x + 2*c*x^2]/(8*c)","A",6,5,15,0.3333,1,"{3467, 3462, 3448, 3352, 3351}"
18,1,100,0,0.0495308,"\int \sin ^2\left(a+b x+c x^2\right) \, dx","Int[Sin[a + b*x + c*x^2]^2,x]","-\frac{\sqrt{\pi } \cos \left(2 a-\frac{b^2}{2 c}\right) \text{FresnelC}\left(\frac{b+2 c x}{\sqrt{\pi } \sqrt{c}}\right)}{4 \sqrt{c}}+\frac{\sqrt{\pi } \sin \left(2 a-\frac{b^2}{2 c}\right) S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{\pi }}\right)}{4 \sqrt{c}}+\frac{x}{2}","-\frac{\sqrt{\pi } \cos \left(2 a-\frac{b^2}{2 c}\right) \text{FresnelC}\left(\frac{b+2 c x}{\sqrt{\pi } \sqrt{c}}\right)}{4 \sqrt{c}}+\frac{\sqrt{\pi } \sin \left(2 a-\frac{b^2}{2 c}\right) S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{\pi }}\right)}{4 \sqrt{c}}+\frac{x}{2}",1,"x/2 - (Sqrt[Pi]*Cos[2*a - b^2/(2*c)]*FresnelC[(b + 2*c*x)/(Sqrt[c]*Sqrt[Pi])])/(4*Sqrt[c]) + (Sqrt[Pi]*FresnelS[(b + 2*c*x)/(Sqrt[c]*Sqrt[Pi])]*Sin[2*a - b^2/(2*c)])/(4*Sqrt[c])","A",5,4,13,0.3077,1,"{3449, 3448, 3352, 3351}"
19,0,0,0,0.0268694,"\int \frac{\sin ^2\left(a+b x+c x^2\right)}{x} \, dx","Int[Sin[a + b*x + c*x^2]^2/x,x]","\int \frac{\sin ^2\left(a+b x+c x^2\right)}{x} \, dx","\frac{\log (x)}{2}-\frac{1}{2} \text{Int}\left(\frac{\cos \left(2 a+2 b x+2 c x^2\right)}{x},x\right)",0,"Log[x]/2 - Defer[Int][Cos[2*a + 2*b*x + 2*c*x^2]/x, x]/2","A",0,0,0,0,-1,"{}"
20,1,248,0,0.2196179,"\int x^2 \sin ^2\left(a+b x-c x^2\right) \, dx","Int[x^2*Sin[a + b*x - c*x^2]^2,x]","\frac{\sqrt{\pi } \sin \left(2 a+\frac{b^2}{2 c}\right) \text{FresnelC}\left(\frac{b-2 c x}{\sqrt{\pi } \sqrt{c}}\right)}{16 c^{3/2}}+\frac{\sqrt{\pi } b^2 \cos \left(2 a+\frac{b^2}{2 c}\right) \text{FresnelC}\left(\frac{b-2 c x}{\sqrt{\pi } \sqrt{c}}\right)}{16 c^{5/2}}+\frac{\sqrt{\pi } b^2 \sin \left(2 a+\frac{b^2}{2 c}\right) S\left(\frac{b-2 c x}{\sqrt{c} \sqrt{\pi }}\right)}{16 c^{5/2}}-\frac{\sqrt{\pi } \cos \left(2 a+\frac{b^2}{2 c}\right) S\left(\frac{b-2 c x}{\sqrt{c} \sqrt{\pi }}\right)}{16 c^{3/2}}+\frac{b \sin \left(2 a+2 b x-2 c x^2\right)}{16 c^2}+\frac{x \sin \left(2 a+2 b x-2 c x^2\right)}{8 c}+\frac{x^3}{6}","\frac{\sqrt{\pi } \sin \left(2 a+\frac{b^2}{2 c}\right) \text{FresnelC}\left(\frac{b-2 c x}{\sqrt{\pi } \sqrt{c}}\right)}{16 c^{3/2}}+\frac{\sqrt{\pi } b^2 \cos \left(2 a+\frac{b^2}{2 c}\right) \text{FresnelC}\left(\frac{b-2 c x}{\sqrt{\pi } \sqrt{c}}\right)}{16 c^{5/2}}+\frac{\sqrt{\pi } b^2 \sin \left(2 a+\frac{b^2}{2 c}\right) S\left(\frac{b-2 c x}{\sqrt{c} \sqrt{\pi }}\right)}{16 c^{5/2}}-\frac{\sqrt{\pi } \cos \left(2 a+\frac{b^2}{2 c}\right) S\left(\frac{b-2 c x}{\sqrt{c} \sqrt{\pi }}\right)}{16 c^{3/2}}+\frac{b \sin \left(2 a+2 b x-2 c x^2\right)}{16 c^2}+\frac{x \sin \left(2 a+2 b x-2 c x^2\right)}{8 c}+\frac{x^3}{6}",1,"x^3/6 + (b^2*Sqrt[Pi]*Cos[2*a + b^2/(2*c)]*FresnelC[(b - 2*c*x)/(Sqrt[c]*Sqrt[Pi])])/(16*c^(5/2)) - (Sqrt[Pi]*Cos[2*a + b^2/(2*c)]*FresnelS[(b - 2*c*x)/(Sqrt[c]*Sqrt[Pi])])/(16*c^(3/2)) + (Sqrt[Pi]*FresnelC[(b - 2*c*x)/(Sqrt[c]*Sqrt[Pi])]*Sin[2*a + b^2/(2*c)])/(16*c^(3/2)) + (b^2*Sqrt[Pi]*FresnelS[(b - 2*c*x)/(Sqrt[c]*Sqrt[Pi])]*Sin[2*a + b^2/(2*c)])/(16*c^(5/2)) + (b*Sin[2*a + 2*b*x - 2*c*x^2])/(16*c^2) + (x*Sin[2*a + 2*b*x - 2*c*x^2])/(8*c)","A",10,7,18,0.3889,1,"{3467, 3464, 3447, 3351, 3352, 3462, 3448}"
21,1,126,0,0.0663787,"\int x \sin ^2\left(a+b x-c x^2\right) \, dx","Int[x*Sin[a + b*x - c*x^2]^2,x]","\frac{\sqrt{\pi } b \cos \left(2 a+\frac{b^2}{2 c}\right) \text{FresnelC}\left(\frac{b-2 c x}{\sqrt{\pi } \sqrt{c}}\right)}{8 c^{3/2}}+\frac{\sqrt{\pi } b \sin \left(2 a+\frac{b^2}{2 c}\right) S\left(\frac{b-2 c x}{\sqrt{c} \sqrt{\pi }}\right)}{8 c^{3/2}}+\frac{\sin \left(2 a+2 b x-2 c x^2\right)}{8 c}+\frac{x^2}{4}","\frac{\sqrt{\pi } b \cos \left(2 a+\frac{b^2}{2 c}\right) \text{FresnelC}\left(\frac{b-2 c x}{\sqrt{\pi } \sqrt{c}}\right)}{8 c^{3/2}}+\frac{\sqrt{\pi } b \sin \left(2 a+\frac{b^2}{2 c}\right) S\left(\frac{b-2 c x}{\sqrt{c} \sqrt{\pi }}\right)}{8 c^{3/2}}+\frac{\sin \left(2 a+2 b x-2 c x^2\right)}{8 c}+\frac{x^2}{4}",1,"x^2/4 + (b*Sqrt[Pi]*Cos[2*a + b^2/(2*c)]*FresnelC[(b - 2*c*x)/(Sqrt[c]*Sqrt[Pi])])/(8*c^(3/2)) + (b*Sqrt[Pi]*FresnelS[(b - 2*c*x)/(Sqrt[c]*Sqrt[Pi])]*Sin[2*a + b^2/(2*c)])/(8*c^(3/2)) + Sin[2*a + 2*b*x - 2*c*x^2]/(8*c)","A",6,5,16,0.3125,1,"{3467, 3462, 3448, 3352, 3351}"
22,1,100,0,0.0478904,"\int \sin ^2\left(a+b x-c x^2\right) \, dx","Int[Sin[a + b*x - c*x^2]^2,x]","\frac{\sqrt{\pi } \cos \left(2 a+\frac{b^2}{2 c}\right) \text{FresnelC}\left(\frac{b-2 c x}{\sqrt{\pi } \sqrt{c}}\right)}{4 \sqrt{c}}+\frac{\sqrt{\pi } \sin \left(2 a+\frac{b^2}{2 c}\right) S\left(\frac{b-2 c x}{\sqrt{c} \sqrt{\pi }}\right)}{4 \sqrt{c}}+\frac{x}{2}","\frac{\sqrt{\pi } \cos \left(2 a+\frac{b^2}{2 c}\right) \text{FresnelC}\left(\frac{b-2 c x}{\sqrt{\pi } \sqrt{c}}\right)}{4 \sqrt{c}}+\frac{\sqrt{\pi } \sin \left(2 a+\frac{b^2}{2 c}\right) S\left(\frac{b-2 c x}{\sqrt{c} \sqrt{\pi }}\right)}{4 \sqrt{c}}+\frac{x}{2}",1,"x/2 + (Sqrt[Pi]*Cos[2*a + b^2/(2*c)]*FresnelC[(b - 2*c*x)/(Sqrt[c]*Sqrt[Pi])])/(4*Sqrt[c]) + (Sqrt[Pi]*FresnelS[(b - 2*c*x)/(Sqrt[c]*Sqrt[Pi])]*Sin[2*a + b^2/(2*c)])/(4*Sqrt[c])","A",5,4,14,0.2857,1,"{3449, 3448, 3352, 3351}"
23,0,0,0,0.0282692,"\int \frac{\sin ^2\left(a+b x-c x^2\right)}{x} \, dx","Int[Sin[a + b*x - c*x^2]^2/x,x]","\int \frac{\sin ^2\left(a+b x-c x^2\right)}{x} \, dx","\frac{\log (x)}{2}-\frac{1}{2} \text{Int}\left(\frac{\cos \left(2 a+2 b x-2 c x^2\right)}{x},x\right)",0,"Log[x]/2 - Defer[Int][Cos[2*a + 2*b*x - 2*c*x^2]/x, x]/2","A",0,0,0,0,-1,"{}"
24,1,85,0,0.0619234,"\int x^2 \sin ^2\left(\frac{1}{4}+x+x^2\right) \, dx","Int[x^2*Sin[1/4 + x + x^2]^2,x]","-\frac{1}{16} \sqrt{\pi } \text{FresnelC}\left(\frac{2 x+1}{\sqrt{\pi }}\right)+\frac{1}{16} \sqrt{\pi } S\left(\frac{2 x+1}{\sqrt{\pi }}\right)+\frac{x^3}{6}-\frac{1}{8} x \sin \left(2 x^2+2 x+\frac{1}{2}\right)+\frac{1}{16} \sin \left(2 x^2+2 x+\frac{1}{2}\right)","-\frac{1}{16} \sqrt{\pi } \text{FresnelC}\left(\frac{2 x+1}{\sqrt{\pi }}\right)+\frac{1}{16} \sqrt{\pi } S\left(\frac{2 x+1}{\sqrt{\pi }}\right)+\frac{x^3}{6}-\frac{1}{8} x \sin \left(2 x^2+2 x+\frac{1}{2}\right)+\frac{1}{16} \sin \left(2 x^2+2 x+\frac{1}{2}\right)",1,"x^3/6 - (Sqrt[Pi]*FresnelC[(1 + 2*x)/Sqrt[Pi]])/16 + (Sqrt[Pi]*FresnelS[(1 + 2*x)/Sqrt[Pi]])/16 + Sin[1/2 + 2*x + 2*x^2]/16 - (x*Sin[1/2 + 2*x + 2*x^2])/8","A",8,7,15,0.4667,1,"{3467, 3464, 3445, 3351, 3462, 3446, 3352}"
25,1,46,0,0.0304473,"\int x \sin ^2\left(\frac{1}{4}+x+x^2\right) \, dx","Int[x*Sin[1/4 + x + x^2]^2,x]","\frac{1}{8} \sqrt{\pi } \text{FresnelC}\left(\frac{2 x+1}{\sqrt{\pi }}\right)+\frac{x^2}{4}-\frac{1}{8} \sin \left(2 x^2+2 x+\frac{1}{2}\right)","\frac{1}{8} \sqrt{\pi } \text{FresnelC}\left(\frac{2 x+1}{\sqrt{\pi }}\right)+\frac{x^2}{4}-\frac{1}{8} \sin \left(2 x^2+2 x+\frac{1}{2}\right)",1,"x^2/4 + (Sqrt[Pi]*FresnelC[(1 + 2*x)/Sqrt[Pi]])/8 - Sin[1/2 + 2*x + 2*x^2]/8","A",5,4,13,0.3077,1,"{3467, 3462, 3446, 3352}"
26,1,27,0,0.0146485,"\int \sin ^2\left(\frac{1}{4}+x+x^2\right) \, dx","Int[Sin[1/4 + x + x^2]^2,x]","\frac{x}{2}-\frac{1}{4} \sqrt{\pi } \text{FresnelC}\left(\frac{2 x+1}{\sqrt{\pi }}\right)","\frac{x}{2}-\frac{1}{4} \sqrt{\pi } \text{FresnelC}\left(\frac{2 x+1}{\sqrt{\pi }}\right)",1,"x/2 - (Sqrt[Pi]*FresnelC[(1 + 2*x)/Sqrt[Pi]])/4","A",4,3,11,0.2727,1,"{3449, 3446, 3352}"
27,0,0,0,0.0275321,"\int \frac{\sin ^2\left(\frac{1}{4}+x+x^2\right)}{x} \, dx","Int[Sin[1/4 + x + x^2]^2/x,x]","\int \frac{\sin ^2\left(\frac{1}{4}+x+x^2\right)}{x} \, dx","\frac{\log (x)}{2}-\frac{1}{2} \text{Int}\left(\frac{\cos \left(2 x^2+2 x+\frac{1}{2}\right)}{x},x\right)",0,"Log[x]/2 - Defer[Int][Cos[1/2 + 2*x + 2*x^2]/x, x]/2","A",0,0,0,0,-1,"{}"
28,0,0,0,0.0494996,"\int \frac{\sin ^2\left(\frac{1}{4}+x+x^2\right)}{x^2} \, dx","Int[Sin[1/4 + x + x^2]^2/x^2,x]","\int \frac{\sin ^2\left(\frac{1}{4}+x+x^2\right)}{x^2} \, dx","\text{Int}\left(\frac{\sin \left(2 x^2+2 x+\frac{1}{2}\right)}{x},x\right)+\sqrt{\pi } S\left(\frac{2 x+1}{\sqrt{\pi }}\right)+\frac{\cos \left(2 x^2+2 x+\frac{1}{2}\right)}{2 x}-\frac{1}{2 x}",0,"-1/(2*x) + Cos[1/2 + 2*x + 2*x^2]/(2*x) + Sqrt[Pi]*FresnelS[(1 + 2*x)/Sqrt[Pi]] + Defer[Int][Sin[1/2 + 2*x + 2*x^2]/x, x]","A",0,0,0,0,-1,"{}"
29,1,285,0,0.2708351,"\int (d+e x)^2 \sin \left(a+b x+c x^2\right) \, dx","Int[(d + e*x)^2*Sin[a + b*x + c*x^2],x]","\frac{\sqrt{\frac{\pi }{2}} \sin \left(a-\frac{b^2}{4 c}\right) (2 c d-b e)^2 \text{FresnelC}\left(\frac{b+2 c x}{\sqrt{2 \pi } \sqrt{c}}\right)}{4 c^{5/2}}+\frac{\sqrt{\frac{\pi }{2}} \cos \left(a-\frac{b^2}{4 c}\right) (2 c d-b e)^2 S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)}{4 c^{5/2}}+\frac{\sqrt{\frac{\pi }{2}} e^2 \cos \left(a-\frac{b^2}{4 c}\right) \text{FresnelC}\left(\frac{b+2 c x}{\sqrt{2 \pi } \sqrt{c}}\right)}{2 c^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} e^2 \sin \left(a-\frac{b^2}{4 c}\right) S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)}{2 c^{3/2}}-\frac{e (2 c d-b e) \cos \left(a+b x+c x^2\right)}{4 c^2}-\frac{e (d+e x) \cos \left(a+b x+c x^2\right)}{2 c}","\frac{\sqrt{\frac{\pi }{2}} \sin \left(a-\frac{b^2}{4 c}\right) (2 c d-b e)^2 \text{FresnelC}\left(\frac{b+2 c x}{\sqrt{2 \pi } \sqrt{c}}\right)}{4 c^{5/2}}+\frac{\sqrt{\frac{\pi }{2}} \cos \left(a-\frac{b^2}{4 c}\right) (2 c d-b e)^2 S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)}{4 c^{5/2}}+\frac{\sqrt{\frac{\pi }{2}} e^2 \cos \left(a-\frac{b^2}{4 c}\right) \text{FresnelC}\left(\frac{b+2 c x}{\sqrt{2 \pi } \sqrt{c}}\right)}{2 c^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} e^2 \sin \left(a-\frac{b^2}{4 c}\right) S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)}{2 c^{3/2}}-\frac{e (2 c d-b e) \cos \left(a+b x+c x^2\right)}{4 c^2}-\frac{e (d+e x) \cos \left(a+b x+c x^2\right)}{2 c}",1,"-(e*(2*c*d - b*e)*Cos[a + b*x + c*x^2])/(4*c^2) - (e*(d + e*x)*Cos[a + b*x + c*x^2])/(2*c) + (e^2*Sqrt[Pi/2]*Cos[a - b^2/(4*c)]*FresnelC[(b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])])/(2*c^(3/2)) + ((2*c*d - b*e)^2*Sqrt[Pi/2]*Cos[a - b^2/(4*c)]*FresnelS[(b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])])/(4*c^(5/2)) + ((2*c*d - b*e)^2*Sqrt[Pi/2]*FresnelC[(b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])]*Sin[a - b^2/(4*c)])/(4*c^(5/2)) - (e^2*Sqrt[Pi/2]*FresnelS[(b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])]*Sin[a - b^2/(4*c)])/(2*c^(3/2))","A",8,6,19,0.3158,1,"{3463, 3448, 3352, 3351, 3461, 3447}"
30,1,140,0,0.0558215,"\int (d+e x) \sin \left(a+b x+c x^2\right) \, dx","Int[(d + e*x)*Sin[a + b*x + c*x^2],x]","\frac{\sqrt{\frac{\pi }{2}} \sin \left(a-\frac{b^2}{4 c}\right) (2 c d-b e) \text{FresnelC}\left(\frac{b+2 c x}{\sqrt{2 \pi } \sqrt{c}}\right)}{2 c^{3/2}}+\frac{\sqrt{\frac{\pi }{2}} \cos \left(a-\frac{b^2}{4 c}\right) (2 c d-b e) S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)}{2 c^{3/2}}-\frac{e \cos \left(a+b x+c x^2\right)}{2 c}","\frac{\sqrt{\frac{\pi }{2}} \sin \left(a-\frac{b^2}{4 c}\right) (2 c d-b e) \text{FresnelC}\left(\frac{b+2 c x}{\sqrt{2 \pi } \sqrt{c}}\right)}{2 c^{3/2}}+\frac{\sqrt{\frac{\pi }{2}} \cos \left(a-\frac{b^2}{4 c}\right) (2 c d-b e) S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)}{2 c^{3/2}}-\frac{e \cos \left(a+b x+c x^2\right)}{2 c}",1,"-(e*Cos[a + b*x + c*x^2])/(2*c) + ((2*c*d - b*e)*Sqrt[Pi/2]*Cos[a - b^2/(4*c)]*FresnelS[(b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])])/(2*c^(3/2)) + ((2*c*d - b*e)*Sqrt[Pi/2]*FresnelC[(b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])]*Sin[a - b^2/(4*c)])/(2*c^(3/2))","A",4,4,17,0.2353,1,"{3461, 3447, 3351, 3352}"
31,1,97,0,0.0221977,"\int \sin \left(a+b x+c x^2\right) \, dx","Int[Sin[a + b*x + c*x^2],x]","\frac{\sqrt{\frac{\pi }{2}} \sin \left(a-\frac{b^2}{4 c}\right) \text{FresnelC}\left(\frac{b+2 c x}{\sqrt{2 \pi } \sqrt{c}}\right)}{\sqrt{c}}+\frac{\sqrt{\frac{\pi }{2}} \cos \left(a-\frac{b^2}{4 c}\right) S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)}{\sqrt{c}}","\frac{\sqrt{\frac{\pi }{2}} \sin \left(a-\frac{b^2}{4 c}\right) \text{FresnelC}\left(\frac{b+2 c x}{\sqrt{2 \pi } \sqrt{c}}\right)}{\sqrt{c}}+\frac{\sqrt{\frac{\pi }{2}} \cos \left(a-\frac{b^2}{4 c}\right) S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)}{\sqrt{c}}",1,"(Sqrt[Pi/2]*Cos[a - b^2/(4*c)]*FresnelS[(b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])])/Sqrt[c] + (Sqrt[Pi/2]*FresnelC[(b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])]*Sin[a - b^2/(4*c)])/Sqrt[c]","A",3,3,11,0.2727,1,"{3447, 3351, 3352}"
32,0,0,0,0.0113595,"\int \frac{\sin \left(a+b x+c x^2\right)}{d+e x} \, dx","Int[Sin[a + b*x + c*x^2]/(d + e*x),x]","\int \frac{\sin \left(a+b x+c x^2\right)}{d+e x} \, dx","\text{Int}\left(\frac{\sin \left(a+b x+c x^2\right)}{d+e x},x\right)",0,"Defer[Int][Sin[a + b*x + c*x^2]/(d + e*x), x]","A",0,0,0,0,-1,"{}"
33,1,291,0,0.3374174,"\int (d+e x)^2 \sin ^2\left(a+b x+c x^2\right) \, dx","Int[(d + e*x)^2*Sin[a + b*x + c*x^2]^2,x]","-\frac{\sqrt{\pi } \cos \left(2 a-\frac{b^2}{2 c}\right) (2 c d-b e)^2 \text{FresnelC}\left(\frac{b+2 c x}{\sqrt{\pi } \sqrt{c}}\right)}{16 c^{5/2}}+\frac{\sqrt{\pi } \sin \left(2 a-\frac{b^2}{2 c}\right) (2 c d-b e)^2 S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{\pi }}\right)}{16 c^{5/2}}+\frac{\sqrt{\pi } e^2 \sin \left(2 a-\frac{b^2}{2 c}\right) \text{FresnelC}\left(\frac{b+2 c x}{\sqrt{\pi } \sqrt{c}}\right)}{16 c^{3/2}}+\frac{\sqrt{\pi } e^2 \cos \left(2 a-\frac{b^2}{2 c}\right) S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{\pi }}\right)}{16 c^{3/2}}-\frac{e (2 c d-b e) \sin \left(2 a+2 b x+2 c x^2\right)}{16 c^2}-\frac{e (d+e x) \sin \left(2 a+2 b x+2 c x^2\right)}{8 c}+\frac{(d+e x)^3}{6 e}","-\frac{\sqrt{\pi } \cos \left(2 a-\frac{b^2}{2 c}\right) (2 c d-b e)^2 \text{FresnelC}\left(\frac{b+2 c x}{\sqrt{\pi } \sqrt{c}}\right)}{16 c^{5/2}}+\frac{\sqrt{\pi } \sin \left(2 a-\frac{b^2}{2 c}\right) (2 c d-b e)^2 S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{\pi }}\right)}{16 c^{5/2}}+\frac{\sqrt{\pi } e^2 \sin \left(2 a-\frac{b^2}{2 c}\right) \text{FresnelC}\left(\frac{b+2 c x}{\sqrt{\pi } \sqrt{c}}\right)}{16 c^{3/2}}+\frac{\sqrt{\pi } e^2 \cos \left(2 a-\frac{b^2}{2 c}\right) S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{\pi }}\right)}{16 c^{3/2}}-\frac{e (2 c d-b e) \sin \left(2 a+2 b x+2 c x^2\right)}{16 c^2}-\frac{e (d+e x) \sin \left(2 a+2 b x+2 c x^2\right)}{8 c}+\frac{(d+e x)^3}{6 e}",1,"(d + e*x)^3/(6*e) - ((2*c*d - b*e)^2*Sqrt[Pi]*Cos[2*a - b^2/(2*c)]*FresnelC[(b + 2*c*x)/(Sqrt[c]*Sqrt[Pi])])/(16*c^(5/2)) + (e^2*Sqrt[Pi]*Cos[2*a - b^2/(2*c)]*FresnelS[(b + 2*c*x)/(Sqrt[c]*Sqrt[Pi])])/(16*c^(3/2)) + (e^2*Sqrt[Pi]*FresnelC[(b + 2*c*x)/(Sqrt[c]*Sqrt[Pi])]*Sin[2*a - b^2/(2*c)])/(16*c^(3/2)) + ((2*c*d - b*e)^2*Sqrt[Pi]*FresnelS[(b + 2*c*x)/(Sqrt[c]*Sqrt[Pi])]*Sin[2*a - b^2/(2*c)])/(16*c^(5/2)) - (e*(2*c*d - b*e)*Sin[2*a + 2*b*x + 2*c*x^2])/(16*c^2) - (e*(d + e*x)*Sin[2*a + 2*b*x + 2*c*x^2])/(8*c)","A",10,7,21,0.3333,1,"{3467, 3464, 3447, 3351, 3352, 3462, 3448}"
34,1,150,0,0.0933062,"\int (d+e x) \sin ^2\left(a+b x+c x^2\right) \, dx","Int[(d + e*x)*Sin[a + b*x + c*x^2]^2,x]","-\frac{\sqrt{\pi } \cos \left(2 a-\frac{b^2}{2 c}\right) (2 c d-b e) \text{FresnelC}\left(\frac{b+2 c x}{\sqrt{\pi } \sqrt{c}}\right)}{8 c^{3/2}}+\frac{\sqrt{\pi } \sin \left(2 a-\frac{b^2}{2 c}\right) (2 c d-b e) S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{\pi }}\right)}{8 c^{3/2}}-\frac{e \sin \left(2 a+2 b x+2 c x^2\right)}{8 c}+\frac{(d+e x)^2}{4 e}","-\frac{\sqrt{\pi } \cos \left(2 a-\frac{b^2}{2 c}\right) (2 c d-b e) \text{FresnelC}\left(\frac{b+2 c x}{\sqrt{\pi } \sqrt{c}}\right)}{8 c^{3/2}}+\frac{\sqrt{\pi } \sin \left(2 a-\frac{b^2}{2 c}\right) (2 c d-b e) S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{\pi }}\right)}{8 c^{3/2}}-\frac{e \sin \left(2 a+2 b x+2 c x^2\right)}{8 c}+\frac{(d+e x)^2}{4 e}",1,"(d + e*x)^2/(4*e) - ((2*c*d - b*e)*Sqrt[Pi]*Cos[2*a - b^2/(2*c)]*FresnelC[(b + 2*c*x)/(Sqrt[c]*Sqrt[Pi])])/(8*c^(3/2)) + ((2*c*d - b*e)*Sqrt[Pi]*FresnelS[(b + 2*c*x)/(Sqrt[c]*Sqrt[Pi])]*Sin[2*a - b^2/(2*c)])/(8*c^(3/2)) - (e*Sin[2*a + 2*b*x + 2*c*x^2])/(8*c)","A",6,5,19,0.2632,1,"{3467, 3462, 3448, 3352, 3351}"
35,1,100,0,0.0484573,"\int \sin ^2\left(a+b x+c x^2\right) \, dx","Int[Sin[a + b*x + c*x^2]^2,x]","-\frac{\sqrt{\pi } \cos \left(2 a-\frac{b^2}{2 c}\right) \text{FresnelC}\left(\frac{b+2 c x}{\sqrt{\pi } \sqrt{c}}\right)}{4 \sqrt{c}}+\frac{\sqrt{\pi } \sin \left(2 a-\frac{b^2}{2 c}\right) S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{\pi }}\right)}{4 \sqrt{c}}+\frac{x}{2}","-\frac{\sqrt{\pi } \cos \left(2 a-\frac{b^2}{2 c}\right) \text{FresnelC}\left(\frac{b+2 c x}{\sqrt{\pi } \sqrt{c}}\right)}{4 \sqrt{c}}+\frac{\sqrt{\pi } \sin \left(2 a-\frac{b^2}{2 c}\right) S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{\pi }}\right)}{4 \sqrt{c}}+\frac{x}{2}",1,"x/2 - (Sqrt[Pi]*Cos[2*a - b^2/(2*c)]*FresnelC[(b + 2*c*x)/(Sqrt[c]*Sqrt[Pi])])/(4*Sqrt[c]) + (Sqrt[Pi]*FresnelS[(b + 2*c*x)/(Sqrt[c]*Sqrt[Pi])]*Sin[2*a - b^2/(2*c)])/(4*Sqrt[c])","A",5,4,13,0.3077,1,"{3449, 3448, 3352, 3351}"
36,0,0,0,0.037116,"\int \frac{\sin ^2\left(a+b x+c x^2\right)}{d+e x} \, dx","Int[Sin[a + b*x + c*x^2]^2/(d + e*x),x]","\int \frac{\sin ^2\left(a+b x+c x^2\right)}{d+e x} \, dx","\frac{\log (d+e x)}{2 e}-\frac{1}{2} \text{Int}\left(\frac{\cos \left(2 a+2 b x+2 c x^2\right)}{d+e x},x\right)",0,"Log[d + e*x]/(2*e) - Defer[Int][Cos[2*a + 2*b*x + 2*c*x^2]/(d + e*x), x]/2","A",0,0,0,0,-1,"{}"