1,1,160,249,0.7019476,"\int x^2 \cos \left(a+b x+c x^2\right) \, dx","Integrate[x^2*Cos[a + b*x + c*x^2],x]","\frac{\sqrt{2 \pi } C\left(\frac{b+2 c x}{\sqrt{c} \sqrt{2 \pi }}\right) \left(b^2 \cos \left(a-\frac{b^2}{4 c}\right)-2 c \sin \left(a-\frac{b^2}{4 c}\right)\right)-\sqrt{2 \pi } S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{2 \pi }}\right) \left(b^2 \sin \left(a-\frac{b^2}{4 c}\right)+2 c \cos \left(a-\frac{b^2}{4 c}\right)\right)+2 \sqrt{c} (2 c x-b) \sin (a+x (b+c x))}{8 c^{5/2}}","-\frac{\sqrt{\frac{\pi }{2}} \sin \left(a-\frac{b^2}{4 c}\right) C\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) C\left(\frac{b+2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)}{4 c^{5/2}}-\frac{\sqrt{\frac{\pi }{2}} b^2 \sin \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{\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)}{2 c^{3/2}}-\frac{b \sin \left(a+b x+c x^2\right)}{4 c^2}+\frac{x \sin \left(a+b x+c x^2\right)}{2 c}",1,"(-(Sqrt[2*Pi]*FresnelS[(b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])]*(2*c*Cos[a - b^2/(4*c)] + b^2*Sin[a - b^2/(4*c)])) + Sqrt[2*Pi]*FresnelC[(b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])]*(b^2*Cos[a - b^2/(4*c)] - 2*c*Sin[a - b^2/(4*c)]) + 2*Sqrt[c]*(-b + 2*c*x)*Sin[a + x*(b + c*x)])/(8*c^(5/2))","A",1
2,1,112,123,0.3023145,"\int x \cos \left(a+b x+c x^2\right) \, dx","Integrate[x*Cos[a + b*x + c*x^2],x]","\frac{\sqrt{2 \pi } (-b) \cos \left(a-\frac{b^2}{4 c}\right) C\left(\frac{b+2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)+\sqrt{2 \pi } b \sin \left(a-\frac{b^2}{4 c}\right) S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)+2 \sqrt{c} \sin (a+x (b+c x))}{4 c^{3/2}}","-\frac{\sqrt{\frac{\pi }{2}} b \cos \left(a-\frac{b^2}{4 c}\right) C\left(\frac{b+2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)}{2 c^{3/2}}+\frac{\sqrt{\frac{\pi }{2}} b \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{\sin \left(a+b x+c x^2\right)}{2 c}",1,"(-(b*Sqrt[2*Pi]*Cos[a - b^2/(4*c)]*FresnelC[(b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])]) + b*Sqrt[2*Pi]*FresnelS[(b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])]*Sin[a - b^2/(4*c)] + 2*Sqrt[c]*Sin[a + x*(b + c*x)])/(4*c^(3/2))","A",1
3,1,85,98,0.1722379,"\int \cos \left(a+b x+c x^2\right) \, dx","Integrate[Cos[a + b*x + c*x^2],x]","\frac{\sqrt{\frac{\pi }{2}} \left(\cos \left(a-\frac{b^2}{4 c}\right) C\left(\frac{b+2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)-\sin \left(a-\frac{b^2}{4 c}\right) S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)\right)}{\sqrt{c}}","\frac{\sqrt{\frac{\pi }{2}} \cos \left(a-\frac{b^2}{4 c}\right) C\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) 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)]*FresnelC[(b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])] - FresnelS[(b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])]*Sin[a - b^2/(4*c)]))/Sqrt[c]","A",1
4,0,0,18,3.6947596,"\int \frac{\cos \left(a+b x+c x^2\right)}{x} \, dx","Integrate[Cos[a + b*x + c*x^2]/x,x]","\int \frac{\cos \left(a+b x+c x^2\right)}{x} \, dx","\text{Int}\left(\frac{\cos \left(a+b x+c x^2\right)}{x},x\right)",0,"Integrate[Cos[a + b*x + c*x^2]/x, x]","A",-1
5,1,110,111,3.3466912,"\int \left(\frac{\cos \left(a+b x+c x^2\right)}{x^2}+\frac{b \sin \left(a+b x+c x^2\right)}{x}\right) \, dx","Integrate[Cos[a + b*x + c*x^2]/x^2 + (b*Sin[a + b*x + c*x^2])/x,x]","-\frac{\sqrt{2 \pi } \sqrt{c} x \sin \left(a-\frac{b^2}{4 c}\right) C\left(\frac{b+2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)+\sqrt{2 \pi } \sqrt{c} x \cos \left(a-\frac{b^2}{4 c}\right) S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)+\cos (a+x (b+c x))}{x}","-\sqrt{2 \pi } \sqrt{c} \sin \left(a-\frac{b^2}{4 c}\right) C\left(\frac{b+2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)-\sqrt{2 \pi } \sqrt{c} \cos \left(a-\frac{b^2}{4 c}\right) S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)-\frac{\cos \left(a+b x+c x^2\right)}{x}",1,"-((Cos[a + x*(b + c*x)] + Sqrt[c]*Sqrt[2*Pi]*x*Cos[a - b^2/(4*c)]*FresnelS[(b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])] + Sqrt[c]*Sqrt[2*Pi]*x*FresnelC[(b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])]*Sin[a - b^2/(4*c)])/x)","A",1
6,1,164,251,0.7129016,"\int x^2 \cos \left(a+b x-c x^2\right) \, dx","Integrate[x^2*Cos[a + b*x - c*x^2],x]","\frac{\sqrt{2 \pi } C\left(\frac{2 c x-b}{\sqrt{c} \sqrt{2 \pi }}\right) \left(2 c \sin \left(a+\frac{b^2}{4 c}\right)+b^2 \cos \left(a+\frac{b^2}{4 c}\right)\right)-\sqrt{2 \pi } S\left(\frac{2 c x-b}{\sqrt{c} \sqrt{2 \pi }}\right) \left(2 c \cos \left(a+\frac{b^2}{4 c}\right)-b^2 \sin \left(a+\frac{b^2}{4 c}\right)\right)-2 \sqrt{c} (b+2 c x) \sin (a+x (b-c x))}{8 c^{5/2}}","-\frac{\sqrt{\frac{\pi }{2}} \sin \left(a+\frac{b^2}{4 c}\right) C\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) C\left(\frac{b-2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)}{4 c^{5/2}}-\frac{\sqrt{\frac{\pi }{2}} b^2 \sin \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{\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)}{2 c^{3/2}}-\frac{b \sin \left(a+b x-c x^2\right)}{4 c^2}-\frac{x \sin \left(a+b x-c x^2\right)}{2 c}",1,"(-(Sqrt[2*Pi]*FresnelS[(-b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])]*(2*c*Cos[a + b^2/(4*c)] - b^2*Sin[a + b^2/(4*c)])) + Sqrt[2*Pi]*FresnelC[(-b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])]*(b^2*Cos[a + b^2/(4*c)] + 2*c*Sin[a + b^2/(4*c)]) - 2*Sqrt[c]*(b + 2*c*x)*Sin[a + x*(b - c*x)])/(8*c^(5/2))","A",1
7,1,116,124,0.3158846,"\int x \cos \left(a+b x-c x^2\right) \, dx","Integrate[x*Cos[a + b*x - c*x^2],x]","\frac{\sqrt{2 \pi } b \cos \left(a+\frac{b^2}{4 c}\right) C\left(\frac{2 c x-b}{\sqrt{c} \sqrt{2 \pi }}\right)+\sqrt{2 \pi } b \sin \left(a+\frac{b^2}{4 c}\right) S\left(\frac{2 c x-b}{\sqrt{c} \sqrt{2 \pi }}\right)-2 \sqrt{c} \sin (a+x (b-c x))}{4 c^{3/2}}","-\frac{\sqrt{\frac{\pi }{2}} b \cos \left(a+\frac{b^2}{4 c}\right) C\left(\frac{b-2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)}{2 c^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} b \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{\sin \left(a+b x-c x^2\right)}{2 c}",1,"(b*Sqrt[2*Pi]*Cos[a + b^2/(4*c)]*FresnelC[(-b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])] + b*Sqrt[2*Pi]*FresnelS[(-b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])]*Sin[a + b^2/(4*c)] - 2*Sqrt[c]*Sin[a + x*(b - c*x)])/(4*c^(3/2))","A",1
8,1,88,99,0.1750193,"\int \cos \left(a+b x-c x^2\right) \, dx","Integrate[Cos[a + b*x - c*x^2],x]","\frac{\sqrt{\frac{\pi }{2}} \left(\cos \left(a+\frac{b^2}{4 c}\right) C\left(\frac{2 c x-b}{\sqrt{c} \sqrt{2 \pi }}\right)+\sin \left(a+\frac{b^2}{4 c}\right) S\left(\frac{2 c x-b}{\sqrt{c} \sqrt{2 \pi }}\right)\right)}{\sqrt{c}}","-\frac{\sqrt{\frac{\pi }{2}} \cos \left(a+\frac{b^2}{4 c}\right) C\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) 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)]*FresnelC[(-b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])] + FresnelS[(-b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])]*Sin[a + b^2/(4*c)]))/Sqrt[c]","A",1
9,0,0,19,3.4878838,"\int \frac{\cos \left(a+b x-c x^2\right)}{x} \, dx","Integrate[Cos[a + b*x - c*x^2]/x,x]","\int \frac{\cos \left(a+b x-c x^2\right)}{x} \, dx","\text{Int}\left(\frac{\cos \left(a+b x-c x^2\right)}{x},x\right)",0,"Integrate[Cos[a + b*x - c*x^2]/x, x]","A",-1
10,1,114,111,4.1217913,"\int \left(\frac{\cos \left(a+b x-c x^2\right)}{x^2}+\frac{b \sin \left(a+b x-c x^2\right)}{x}\right) \, dx","Integrate[Cos[a + b*x - c*x^2]/x^2 + (b*Sin[a + b*x - c*x^2])/x,x]","\sqrt{2 \pi } \sqrt{c} \sin \left(a+\frac{b^2}{4 c}\right) C\left(\frac{2 c x-b}{\sqrt{c} \sqrt{2 \pi }}\right)-\sqrt{2 \pi } \sqrt{c} \cos \left(a+\frac{b^2}{4 c}\right) S\left(\frac{2 c x-b}{\sqrt{c} \sqrt{2 \pi }}\right)-\frac{\cos (a+x (b-c x))}{x}","-\sqrt{2 \pi } \sqrt{c} \sin \left(a+\frac{b^2}{4 c}\right) C\left(\frac{b-2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)+\sqrt{2 \pi } \sqrt{c} \cos \left(a+\frac{b^2}{4 c}\right) S\left(\frac{b-2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)-\frac{\cos \left(a+b x-c x^2\right)}{x}",1,"-(Cos[a + x*(b - c*x)]/x) - Sqrt[c]*Sqrt[2*Pi]*Cos[a + b^2/(4*c)]*FresnelS[(-b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])] + Sqrt[c]*Sqrt[2*Pi]*FresnelC[(-b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])]*Sin[a + b^2/(4*c)]","A",1
11,1,67,82,0.1406693,"\int x^2 \cos \left(\frac{1}{4}+x+x^2\right) \, dx","Integrate[x^2*Cos[1/4 + x + x^2],x]","\frac{1}{8} \left(\sqrt{2 \pi } C\left(\frac{2 x+1}{\sqrt{2 \pi }}\right)-2 \left(\sqrt{2 \pi } S\left(\frac{2 x+1}{\sqrt{2 \pi }}\right)+(1-2 x) \sin \left(x^2+x+\frac{1}{4}\right)\right)\right)","\frac{1}{4} \sqrt{\frac{\pi }{2}} C\left(\frac{2 x+1}{\sqrt{2 \pi }}\right)-\frac{1}{2} \sqrt{\frac{\pi }{2}} S\left(\frac{2 x+1}{\sqrt{2 \pi }}\right)+\frac{1}{2} x \sin \left(x^2+x+\frac{1}{4}\right)-\frac{1}{4} \sin \left(x^2+x+\frac{1}{4}\right)",1,"(Sqrt[2*Pi]*FresnelC[(1 + 2*x)/Sqrt[2*Pi]] - 2*(Sqrt[2*Pi]*FresnelS[(1 + 2*x)/Sqrt[2*Pi]] + (1 - 2*x)*Sin[1/4 + x + x^2]))/8","A",1
12,1,39,41,0.047858,"\int x \cos \left(\frac{1}{4}+x+x^2\right) \, dx","Integrate[x*Cos[1/4 + x + x^2],x]","\frac{1}{4} \left(2 \sin \left(x^2+x+\frac{1}{4}\right)-\sqrt{2 \pi } C\left(\frac{2 x+1}{\sqrt{2 \pi }}\right)\right)","\frac{1}{2} \sin \left(x^2+x+\frac{1}{4}\right)-\frac{1}{2} \sqrt{\frac{\pi }{2}} C\left(\frac{2 x+1}{\sqrt{2 \pi }}\right)",1,"(-(Sqrt[2*Pi]*FresnelC[(1 + 2*x)/Sqrt[2*Pi]]) + 2*Sin[1/4 + x + x^2])/4","A",1
13,1,24,24,0.0242869,"\int \cos \left(\frac{1}{4}+x+x^2\right) \, dx","Integrate[Cos[1/4 + x + x^2],x]","\sqrt{\frac{\pi }{2}} C\left(\frac{2 x+1}{\sqrt{2 \pi }}\right)","\sqrt{\frac{\pi }{2}} C\left(\frac{2 x+1}{\sqrt{2 \pi }}\right)",1,"Sqrt[Pi/2]*FresnelC[(1 + 2*x)/Sqrt[2*Pi]]","A",1
14,0,0,16,11.0430622,"\int \frac{\cos \left(\frac{1}{4}+x+x^2\right)}{x} \, dx","Integrate[Cos[1/4 + x + x^2]/x,x]","\int \frac{\cos \left(\frac{1}{4}+x+x^2\right)}{x} \, dx","\text{Int}\left(\frac{\cos \left(x^2+x+\frac{1}{4}\right)}{x},x\right)",0,"Integrate[Cos[1/4 + x + x^2]/x, x]","A",-1
15,0,0,56,12.2060147,"\int \frac{\cos \left(\frac{1}{4}+x+x^2\right)}{x^2} \, dx","Integrate[Cos[1/4 + x + x^2]/x^2,x]","\int \frac{\cos \left(\frac{1}{4}+x+x^2\right)}{x^2} \, dx","-\text{Int}\left(\frac{\sin \left(x^2+x+\frac{1}{4}\right)}{x},x\right)-\sqrt{2 \pi } S\left(\frac{2 x+1}{\sqrt{2 \pi }}\right)-\frac{\cos \left(x^2+x+\frac{1}{4}\right)}{x}",0,"Integrate[Cos[1/4 + x + x^2]/x^2, x]","A",-1
16,1,170,248,0.6609237,"\int x^2 \cos ^2\left(a+b x+c x^2\right) \, dx","Integrate[x^2*Cos[a + b*x + c*x^2]^2,x]","\frac{3 \sqrt{\pi } C\left(\frac{b+2 c x}{\sqrt{c} \sqrt{\pi }}\right) \left(b^2 \cos \left(2 a-\frac{b^2}{2 c}\right)-c \sin \left(2 a-\frac{b^2}{2 c}\right)\right)-3 \sqrt{\pi } S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{\pi }}\right) \left(b^2 \sin \left(2 a-\frac{b^2}{2 c}\right)+c \cos \left(2 a-\frac{b^2}{2 c}\right)\right)+\sqrt{c} \left(8 c^2 x^3-3 (b-2 c x) \sin (2 (a+x (b+c x)))\right)}{48 c^{5/2}}","-\frac{\sqrt{\pi } \sin \left(2 a-\frac{b^2}{2 c}\right) C\left(\frac{b+2 c x}{\sqrt{c} \sqrt{\pi }}\right)}{16 c^{3/2}}+\frac{\sqrt{\pi } b^2 \cos \left(2 a-\frac{b^2}{2 c}\right) C\left(\frac{b+2 c x}{\sqrt{c} \sqrt{\pi }}\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,"(-3*Sqrt[Pi]*FresnelS[(b + 2*c*x)/(Sqrt[c]*Sqrt[Pi])]*(c*Cos[2*a - b^2/(2*c)] + b^2*Sin[2*a - b^2/(2*c)]) + 3*Sqrt[Pi]*FresnelC[(b + 2*c*x)/(Sqrt[c]*Sqrt[Pi])]*(b^2*Cos[2*a - b^2/(2*c)] - c*Sin[2*a - b^2/(2*c)]) + Sqrt[c]*(8*c^2*x^3 - 3*(b - 2*c*x)*Sin[2*(a + x*(b + c*x))]))/(48*c^(5/2))","A",1
17,1,116,126,0.2676669,"\int x \cos ^2\left(a+b x+c x^2\right) \, dx","Integrate[x*Cos[a + b*x + c*x^2]^2,x]","\frac{\sqrt{\pi } (-b) \cos \left(2 a-\frac{b^2}{2 c}\right) C\left(\frac{b+2 c x}{\sqrt{c} \sqrt{\pi }}\right)+\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)+\sqrt{c} \left(\sin (2 (a+x (b+c x)))+2 c x^2\right)}{8 c^{3/2}}","-\frac{\sqrt{\pi } b \cos \left(2 a-\frac{b^2}{2 c}\right) C\left(\frac{b+2 c x}{\sqrt{c} \sqrt{\pi }}\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,"(-(b*Sqrt[Pi]*Cos[2*a - b^2/(2*c)]*FresnelC[(b + 2*c*x)/(Sqrt[c]*Sqrt[Pi])]) + b*Sqrt[Pi]*FresnelS[(b + 2*c*x)/(Sqrt[c]*Sqrt[Pi])]*Sin[2*a - b^2/(2*c)] + Sqrt[c]*(2*c*x^2 + Sin[2*(a + x*(b + c*x))]))/(8*c^(3/2))","A",1
18,1,97,100,0.1032822,"\int \cos ^2\left(a+b x+c x^2\right) \, dx","Integrate[Cos[a + b*x + c*x^2]^2,x]","\frac{\sqrt{\pi } \cos \left(2 a-\frac{b^2}{2 c}\right) C\left(\frac{b+2 c x}{\sqrt{c} \sqrt{\pi }}\right)-\sqrt{\pi } \sin \left(2 a-\frac{b^2}{2 c}\right) S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{\pi }}\right)+2 \sqrt{c} x}{4 \sqrt{c}}","\frac{\sqrt{\pi } \cos \left(2 a-\frac{b^2}{2 c}\right) C\left(\frac{b+2 c x}{\sqrt{c} \sqrt{\pi }}\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,"(2*Sqrt[c]*x + Sqrt[Pi]*Cos[2*a - b^2/(2*c)]*FresnelC[(b + 2*c*x)/(Sqrt[c]*Sqrt[Pi])] - Sqrt[Pi]*FresnelS[(b + 2*c*x)/(Sqrt[c]*Sqrt[Pi])]*Sin[2*a - b^2/(2*c)])/(4*Sqrt[c])","A",1
19,0,0,33,6.397256,"\int \frac{\cos ^2\left(a+b x+c x^2\right)}{x} \, dx","Integrate[Cos[a + b*x + c*x^2]^2/x,x]","\int \frac{\cos ^2\left(a+b x+c x^2\right)}{x} \, dx","\frac{1}{2} \text{Int}\left(\frac{\cos \left(2 a+2 b x+2 c x^2\right)}{x},x\right)+\frac{\log (x)}{2}",0,"Integrate[Cos[a + b*x + c*x^2]^2/x, x]","A",-1
20,1,175,248,0.6587853,"\int x^2 \cos ^2\left(a+b x-c x^2\right) \, dx","Integrate[x^2*Cos[a + b*x - c*x^2]^2,x]","\frac{3 \sqrt{\pi } C\left(\frac{2 c x-b}{\sqrt{c} \sqrt{\pi }}\right) \left(c \sin \left(2 a+\frac{b^2}{2 c}\right)+b^2 \cos \left(2 a+\frac{b^2}{2 c}\right)\right)-3 \sqrt{\pi } S\left(\frac{2 c x-b}{\sqrt{c} \sqrt{\pi }}\right) \left(c \cos \left(2 a+\frac{b^2}{2 c}\right)-b^2 \sin \left(2 a+\frac{b^2}{2 c}\right)\right)+\sqrt{c} \left(8 c^2 x^3-3 (b+2 c x) \sin (2 (a+x (b-c x)))\right)}{48 c^{5/2}}","-\frac{\sqrt{\pi } \sin \left(2 a+\frac{b^2}{2 c}\right) C\left(\frac{b-2 c x}{\sqrt{c} \sqrt{\pi }}\right)}{16 c^{3/2}}-\frac{\sqrt{\pi } b^2 \cos \left(2 a+\frac{b^2}{2 c}\right) C\left(\frac{b-2 c x}{\sqrt{c} \sqrt{\pi }}\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,"(-3*Sqrt[Pi]*FresnelS[(-b + 2*c*x)/(Sqrt[c]*Sqrt[Pi])]*(c*Cos[2*a + b^2/(2*c)] - b^2*Sin[2*a + b^2/(2*c)]) + 3*Sqrt[Pi]*FresnelC[(-b + 2*c*x)/(Sqrt[c]*Sqrt[Pi])]*(b^2*Cos[2*a + b^2/(2*c)] + c*Sin[2*a + b^2/(2*c)]) + Sqrt[c]*(8*c^2*x^3 - 3*(b + 2*c*x)*Sin[2*(a + x*(b - c*x))]))/(48*c^(5/2))","A",1
21,1,122,126,0.2831353,"\int x \cos ^2\left(a+b x-c x^2\right) \, dx","Integrate[x*Cos[a + b*x - c*x^2]^2,x]","\frac{\sqrt{\pi } b \cos \left(2 a+\frac{b^2}{2 c}\right) C\left(\frac{2 c x-b}{\sqrt{c} \sqrt{\pi }}\right)+\sqrt{\pi } b \sin \left(2 a+\frac{b^2}{2 c}\right) S\left(\frac{2 c x-b}{\sqrt{c} \sqrt{\pi }}\right)+\sqrt{c} \left(2 c x^2-\sin (2 (a+x (b-c x)))\right)}{8 c^{3/2}}","-\frac{\sqrt{\pi } b \cos \left(2 a+\frac{b^2}{2 c}\right) C\left(\frac{b-2 c x}{\sqrt{c} \sqrt{\pi }}\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,"(b*Sqrt[Pi]*Cos[2*a + b^2/(2*c)]*FresnelC[(-b + 2*c*x)/(Sqrt[c]*Sqrt[Pi])] + b*Sqrt[Pi]*FresnelS[(-b + 2*c*x)/(Sqrt[c]*Sqrt[Pi])]*Sin[2*a + b^2/(2*c)] + Sqrt[c]*(2*c*x^2 - Sin[2*(a + x*(b - c*x))]))/(8*c^(3/2))","A",1
22,1,100,100,0.1077651,"\int \cos ^2\left(a+b x-c x^2\right) \, dx","Integrate[Cos[a + b*x - c*x^2]^2,x]","\frac{\sqrt{\pi } \cos \left(2 a+\frac{b^2}{2 c}\right) C\left(\frac{2 c x-b}{\sqrt{c} \sqrt{\pi }}\right)+\sqrt{\pi } \sin \left(2 a+\frac{b^2}{2 c}\right) S\left(\frac{2 c x-b}{\sqrt{c} \sqrt{\pi }}\right)+2 \sqrt{c} x}{4 \sqrt{c}}","-\frac{\sqrt{\pi } \cos \left(2 a+\frac{b^2}{2 c}\right) C\left(\frac{b-2 c x}{\sqrt{c} \sqrt{\pi }}\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,"(2*Sqrt[c]*x + Sqrt[Pi]*Cos[2*a + b^2/(2*c)]*FresnelC[(-b + 2*c*x)/(Sqrt[c]*Sqrt[Pi])] + Sqrt[Pi]*FresnelS[(-b + 2*c*x)/(Sqrt[c]*Sqrt[Pi])]*Sin[2*a + b^2/(2*c)])/(4*Sqrt[c])","A",1
23,0,0,33,6.6887542,"\int \frac{\cos ^2\left(a+b x-c x^2\right)}{x} \, dx","Integrate[Cos[a + b*x - c*x^2]^2/x,x]","\int \frac{\cos ^2\left(a+b x-c x^2\right)}{x} \, dx","\frac{1}{2} \text{Int}\left(\frac{\cos \left(2 a+2 b x-2 c x^2\right)}{x},x\right)+\frac{\log (x)}{2}",0,"Integrate[Cos[a + b*x - c*x^2]^2/x, x]","A",-1
24,1,77,85,0.1478984,"\int x^2 \cos ^2\left(\frac{1}{4}+x+x^2\right) \, dx","Integrate[x^2*Cos[1/4 + x + x^2]^2,x]","\frac{1}{48} \left(3 \sqrt{\pi } C\left(\frac{2 x+1}{\sqrt{\pi }}\right)-3 \sqrt{\pi } S\left(\frac{2 x+1}{\sqrt{\pi }}\right)+8 x^3+6 x \sin \left(\frac{1}{2} (2 x+1)^2\right)-3 \sin \left(\frac{1}{2} (2 x+1)^2\right)\right)","\frac{1}{16} \sqrt{\pi } C\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,"(8*x^3 + 3*Sqrt[Pi]*FresnelC[(1 + 2*x)/Sqrt[Pi]] - 3*Sqrt[Pi]*FresnelS[(1 + 2*x)/Sqrt[Pi]] - 3*Sin[(1 + 2*x)^2/2] + 6*x*Sin[(1 + 2*x)^2/2])/48","A",1
25,1,41,46,0.0575669,"\int x \cos ^2\left(\frac{1}{4}+x+x^2\right) \, dx","Integrate[x*Cos[1/4 + x + x^2]^2,x]","\frac{1}{8} \left(-\sqrt{\pi } C\left(\frac{2 x+1}{\sqrt{\pi }}\right)+2 x^2+\sin \left(\frac{1}{2} (2 x+1)^2\right)\right)","-\frac{1}{8} \sqrt{\pi } C\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,"(2*x^2 - Sqrt[Pi]*FresnelC[(1 + 2*x)/Sqrt[Pi]] + Sin[(1 + 2*x)^2/2])/8","A",1
26,1,26,27,0.0129022,"\int \cos ^2\left(\frac{1}{4}+x+x^2\right) \, dx","Integrate[Cos[1/4 + x + x^2]^2,x]","\frac{1}{4} \left(\sqrt{\pi } C\left(\frac{2 x+1}{\sqrt{\pi }}\right)+2 x\right)","\frac{1}{4} \sqrt{\pi } C\left(\frac{2 x+1}{\sqrt{\pi }}\right)+\frac{x}{2}",1,"(2*x + Sqrt[Pi]*FresnelC[(1 + 2*x)/Sqrt[Pi]])/4","A",1
27,0,0,31,10.4267711,"\int \frac{\cos ^2\left(\frac{1}{4}+x+x^2\right)}{x} \, dx","Integrate[Cos[1/4 + x + x^2]^2/x,x]","\int \frac{\cos ^2\left(\frac{1}{4}+x+x^2\right)}{x} \, dx","\frac{1}{2} \text{Int}\left(\frac{\cos \left(2 x^2+2 x+\frac{1}{2}\right)}{x},x\right)+\frac{\log (x)}{2}",0,"Integrate[Cos[1/4 + x + x^2]^2/x, x]","A",-1
28,0,0,69,10.6464065,"\int \frac{\cos ^2\left(\frac{1}{4}+x+x^2\right)}{x^2} \, dx","Integrate[Cos[1/4 + x + x^2]^2/x^2,x]","\int \frac{\cos ^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,"Integrate[Cos[1/4 + x + x^2]^2/x^2, x]","A",-1
29,1,187,285,1.2663307,"\int (d+e x)^2 \cos \left(a+b x+c x^2\right) \, dx","Integrate[(d + e*x)^2*Cos[a + b*x + c*x^2],x]","\frac{\sqrt{2 \pi } C\left(\frac{b+2 c x}{\sqrt{c} \sqrt{2 \pi }}\right) \left(\cos \left(a-\frac{b^2}{4 c}\right) (b e-2 c d)^2-2 c e^2 \sin \left(a-\frac{b^2}{4 c}\right)\right)-\sqrt{2 \pi } S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{2 \pi }}\right) \left(\sin \left(a-\frac{b^2}{4 c}\right) (b e-2 c d)^2+2 c e^2 \cos \left(a-\frac{b^2}{4 c}\right)\right)+2 \sqrt{c} e \sin (a+x (b+c x)) (-b e+4 c d+2 c e x)}{8 c^{5/2}}","\frac{\sqrt{\frac{\pi }{2}} \cos \left(a-\frac{b^2}{4 c}\right) (2 c d-b e)^2 C\left(\frac{b+2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)}{4 c^{5/2}}-\frac{\sqrt{\frac{\pi }{2}} \sin \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 \sin \left(a-\frac{b^2}{4 c}\right) C\left(\frac{b+2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)}{2 c^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} e^2 \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{e (2 c d-b e) \sin \left(a+b x+c x^2\right)}{4 c^2}+\frac{e (d+e x) \sin \left(a+b x+c x^2\right)}{2 c}",1,"(Sqrt[2*Pi]*FresnelC[(b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])]*((-2*c*d + b*e)^2*Cos[a - b^2/(4*c)] - 2*c*e^2*Sin[a - b^2/(4*c)]) - Sqrt[2*Pi]*FresnelS[(b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])]*(2*c*e^2*Cos[a - b^2/(4*c)] + (-2*c*d + b*e)^2*Sin[a - b^2/(4*c)]) + 2*Sqrt[c]*e*(4*c*d - b*e + 2*c*e*x)*Sin[a + x*(b + c*x)])/(8*c^(5/2))","A",1
30,1,129,140,0.561049,"\int (d+e x) \cos \left(a+b x+c x^2\right) \, dx","Integrate[(d + e*x)*Cos[a + b*x + c*x^2],x]","\frac{\sqrt{2 \pi } \cos \left(a-\frac{b^2}{4 c}\right) (2 c d-b e) C\left(\frac{b+2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)-\sqrt{2 \pi } \sin \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 \sqrt{c} e \sin (a+x (b+c x))}{4 c^{3/2}}","\frac{\sqrt{\frac{\pi }{2}} \cos \left(a-\frac{b^2}{4 c}\right) (2 c d-b e) C\left(\frac{b+2 c x}{\sqrt{c} \sqrt{2 \pi }}\right)}{2 c^{3/2}}-\frac{\sqrt{\frac{\pi }{2}} \sin \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 \sin \left(a+b x+c x^2\right)}{2 c}",1,"((2*c*d - b*e)*Sqrt[2*Pi]*Cos[a - b^2/(4*c)]*FresnelC[(b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])] - (2*c*d - b*e)*Sqrt[2*Pi]*FresnelS[(b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])]*Sin[a - b^2/(4*c)] + 2*Sqrt[c]*e*Sin[a + x*(b + c*x)])/(4*c^(3/2))","A",1
31,0,0,22,6.2712873,"\int \frac{\cos \left(a+b x+c x^2\right)}{d+e x} \, dx","Integrate[Cos[a + b*x + c*x^2]/(d + e*x),x]","\int \frac{\cos \left(a+b x+c x^2\right)}{d+e x} \, dx","\text{Int}\left(\frac{\cos \left(a+b x+c x^2\right)}{d+e x},x\right)",0,"Integrate[Cos[a + b*x + c*x^2]/(d + e*x), x]","A",-1
32,1,215,291,1.1601659,"\int (d+e x)^2 \cos ^2\left(a+b x+c x^2\right) \, dx","Integrate[(d + e*x)^2*Cos[a + b*x + c*x^2]^2,x]","\frac{3 \sqrt{\pi } C\left(\frac{b+2 c x}{\sqrt{c} \sqrt{\pi }}\right) \left(\cos \left(2 a-\frac{b^2}{2 c}\right) (b e-2 c d)^2-c e^2 \sin \left(2 a-\frac{b^2}{2 c}\right)\right)-3 \sqrt{\pi } S\left(\frac{b+2 c x}{\sqrt{c} \sqrt{\pi }}\right) \left(\sin \left(2 a-\frac{b^2}{2 c}\right) (b e-2 c d)^2+c e^2 \cos \left(2 a-\frac{b^2}{2 c}\right)\right)+\sqrt{c} \left(3 e \sin (2 (a+x (b+c x))) (-b e+4 c d+2 c e x)+8 c^2 x \left(3 d^2+3 d e x+e^2 x^2\right)\right)}{48 c^{5/2}}","\frac{\sqrt{\pi } \cos \left(2 a-\frac{b^2}{2 c}\right) (2 c d-b e)^2 C\left(\frac{b+2 c x}{\sqrt{c} \sqrt{\pi }}\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) C\left(\frac{b+2 c x}{\sqrt{c} \sqrt{\pi }}\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,"(3*Sqrt[Pi]*FresnelC[(b + 2*c*x)/(Sqrt[c]*Sqrt[Pi])]*((-2*c*d + b*e)^2*Cos[2*a - b^2/(2*c)] - c*e^2*Sin[2*a - b^2/(2*c)]) - 3*Sqrt[Pi]*FresnelS[(b + 2*c*x)/(Sqrt[c]*Sqrt[Pi])]*(c*e^2*Cos[2*a - b^2/(2*c)] + (-2*c*d + b*e)^2*Sin[2*a - b^2/(2*c)]) + Sqrt[c]*(8*c^2*x*(3*d^2 + 3*d*e*x + e^2*x^2) + 3*e*(4*c*d - b*e + 2*c*e*x)*Sin[2*(a + x*(b + c*x))]))/(48*c^(5/2))","A",1
33,1,139,150,0.4116762,"\int (d+e x) \cos ^2\left(a+b x+c x^2\right) \, dx","Integrate[(d + e*x)*Cos[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) C\left(\frac{b+2 c x}{\sqrt{c} \sqrt{\pi }}\right)-\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)+\sqrt{c} (e \sin (2 (a+x (b+c x)))+2 c x (2 d+e x))}{8 c^{3/2}}","\frac{\sqrt{\pi } \cos \left(2 a-\frac{b^2}{2 c}\right) (2 c d-b e) C\left(\frac{b+2 c x}{\sqrt{c} \sqrt{\pi }}\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,"((2*c*d - b*e)*Sqrt[Pi]*Cos[2*a - b^2/(2*c)]*FresnelC[(b + 2*c*x)/(Sqrt[c]*Sqrt[Pi])] - (2*c*d - b*e)*Sqrt[Pi]*FresnelS[(b + 2*c*x)/(Sqrt[c]*Sqrt[Pi])]*Sin[2*a - b^2/(2*c)] + Sqrt[c]*(2*c*x*(2*d + e*x) + e*Sin[2*(a + x*(b + c*x))]))/(8*c^(3/2))","A",1
34,0,0,44,6.5887995,"\int \frac{\cos ^2\left(a+b x+c x^2\right)}{d+e x} \, dx","Integrate[Cos[a + b*x + c*x^2]^2/(d + e*x),x]","\int \frac{\cos ^2\left(a+b x+c x^2\right)}{d+e x} \, dx","\frac{1}{2} \text{Int}\left(\frac{\cos \left(2 a+2 b x+2 c x^2\right)}{d+e x},x\right)+\frac{\log (d+e x)}{2 e}",0,"Integrate[Cos[a + b*x + c*x^2]^2/(d + e*x), x]","A",-1