1,1,88,124,0.079862,"\int x^7 S(b x) \, dx","Integrate[x^7*FresnelS[b*x],x]","\frac{\left(\pi ^4 b^8 x^8-105\right) S(b x)-7 b x \left(\pi ^2 b^4 x^4-15\right) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)+\pi  b^3 x^3 \left(\pi ^2 b^4 x^4-35\right) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{8 \pi ^4 b^8}","-\frac{105 S(b x)}{8 \pi ^4 b^8}+\frac{x^7 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{8 \pi  b}+\frac{105 x \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{8 \pi ^4 b^7}-\frac{35 x^3 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{8 \pi ^3 b^5}-\frac{7 x^5 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{8 \pi ^2 b^3}+\frac{1}{8} x^8 S(b x)",1,"(b^3*Pi*x^3*(-35 + b^4*Pi^2*x^4)*Cos[(b^2*Pi*x^2)/2] + (-105 + b^8*Pi^4*x^8)*FresnelS[b*x] - 7*b*x*(-15 + b^4*Pi^2*x^4)*Sin[(b^2*Pi*x^2)/2])/(8*b^8*Pi^4)","A",1
2,1,83,109,0.0661776,"\int x^6 S(b x) \, dx","Integrate[x^6*FresnelS[b*x],x]","-\frac{6 \left(\pi ^2 b^4 x^4-8\right) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi ^4 b^7}+\frac{x^2 \left(\pi ^2 b^4 x^4-24\right) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi ^3 b^5}+\frac{1}{7} x^7 S(b x)","\frac{x^6 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi  b}+\frac{48 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi ^4 b^7}-\frac{24 x^2 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi ^3 b^5}-\frac{6 x^4 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi ^2 b^3}+\frac{1}{7} x^7 S(b x)",1,"(x^2*(-24 + b^4*Pi^2*x^4)*Cos[(b^2*Pi*x^2)/2])/(7*b^5*Pi^3) + (x^7*FresnelS[b*x])/7 - (6*(-8 + b^4*Pi^2*x^4)*Sin[(b^2*Pi*x^2)/2])/(7*b^7*Pi^4)","A",1
3,1,79,99,0.0951859,"\int x^5 S(b x) \, dx","Integrate[x^5*FresnelS[b*x],x]","\frac{\pi ^3 b^6 x^6 S(b x)+b x \left(\pi ^2 b^4 x^4-15\right) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)-5 \pi  b^3 x^3 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)+15 C(b x)}{6 \pi ^3 b^6}","\frac{5 C(b x)}{2 \pi ^3 b^6}+\frac{x^5 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 \pi  b}-\frac{5 x \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{2 \pi ^3 b^5}-\frac{5 x^3 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 \pi ^2 b^3}+\frac{1}{6} x^6 S(b x)",1,"(b*x*(-15 + b^4*Pi^2*x^4)*Cos[(b^2*Pi*x^2)/2] + 15*FresnelC[b*x] + b^6*Pi^3*x^6*FresnelS[b*x] - 5*b^3*Pi*x^3*Sin[(b^2*Pi*x^2)/2])/(6*b^6*Pi^3)","A",1
4,1,71,84,0.0468595,"\int x^4 S(b x) \, dx","Integrate[x^4*FresnelS[b*x],x]","-\frac{4 x^2 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 \pi ^2 b^3}+\frac{\left(\pi ^2 b^4 x^4-8\right) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 \pi ^3 b^5}+\frac{1}{5} x^5 S(b x)","\frac{x^4 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 \pi  b}-\frac{8 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 \pi ^3 b^5}-\frac{4 x^2 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 \pi ^2 b^3}+\frac{1}{5} x^5 S(b x)",1,"((-8 + b^4*Pi^2*x^4)*Cos[(b^2*Pi*x^2)/2])/(5*b^5*Pi^3) + (x^5*FresnelS[b*x])/5 - (4*x^2*Sin[(b^2*Pi*x^2)/2])/(5*b^3*Pi^2)","A",1
5,1,74,74,0.0237757,"\int x^3 S(b x) \, dx","Integrate[x^3*FresnelS[b*x],x]","\frac{3 S(b x)}{4 \pi ^2 b^4}+\frac{x^3 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi  b}-\frac{3 x \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi ^2 b^3}+\frac{1}{4} x^4 S(b x)","\frac{3 S(b x)}{4 \pi ^2 b^4}+\frac{x^3 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi  b}-\frac{3 x \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi ^2 b^3}+\frac{1}{4} x^4 S(b x)",1,"(x^3*Cos[(b^2*Pi*x^2)/2])/(4*b*Pi) + (3*FresnelS[b*x])/(4*b^4*Pi^2) + (x^4*FresnelS[b*x])/4 - (3*x*Sin[(b^2*Pi*x^2)/2])/(4*b^3*Pi^2)","A",1
6,1,59,59,0.0151248,"\int x^2 S(b x) \, dx","Integrate[x^2*FresnelS[b*x],x]","\frac{x^2 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 \pi  b}-\frac{2 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 \pi ^2 b^3}+\frac{1}{3} x^3 S(b x)","\frac{x^2 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 \pi  b}-\frac{2 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 \pi ^2 b^3}+\frac{1}{3} x^3 S(b x)",1,"(x^2*Cos[(b^2*Pi*x^2)/2])/(3*b*Pi) + (x^3*FresnelS[b*x])/3 - (2*Sin[(b^2*Pi*x^2)/2])/(3*b^3*Pi^2)","A",1
7,1,49,49,0.0128648,"\int x S(b x) \, dx","Integrate[x*FresnelS[b*x],x]","-\frac{C(b x)}{2 \pi  b^2}+\frac{x \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{2 \pi  b}+\frac{1}{2} x^2 S(b x)","-\frac{C(b x)}{2 \pi  b^2}+\frac{x \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{2 \pi  b}+\frac{1}{2} x^2 S(b x)",1,"(x*Cos[(b^2*Pi*x^2)/2])/(2*b*Pi) - FresnelC[b*x]/(2*b^2*Pi) + (x^2*FresnelS[b*x])/2","A",1
8,1,26,26,0.003778,"\int S(b x) \, dx","Integrate[FresnelS[b*x],x]","\frac{\cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b}+x S(b x)","\frac{\cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b}+x S(b x)",1,"Cos[(b^2*Pi*x^2)/2]/(b*Pi) + x*FresnelS[b*x]","A",1
9,0,0,73,0.0189704,"\int \frac{S(b x)}{x} \, dx","Integrate[FresnelS[b*x]/x,x]","\int \frac{S(b x)}{x} \, dx","\frac{1}{2} i b x \, _2F_2\left(\frac{1}{2},\frac{1}{2};\frac{3}{2},\frac{3}{2};-\frac{1}{2} i b^2 \pi  x^2\right)-\frac{1}{2} i b x \, _2F_2\left(\frac{1}{2},\frac{1}{2};\frac{3}{2},\frac{3}{2};\frac{1}{2} i b^2 \pi  x^2\right)",1,"Integrate[FresnelS[b*x]/x, x]","F",-1
10,1,27,27,0.0152286,"\int \frac{S(b x)}{x^2} \, dx","Integrate[FresnelS[b*x]/x^2,x]","\frac{1}{2} b \text{Si}\left(\frac{1}{2} b^2 \pi  x^2\right)-\frac{S(b x)}{x}","\frac{1}{2} b \text{Si}\left(\frac{1}{2} b^2 \pi  x^2\right)-\frac{S(b x)}{x}",1,"-(FresnelS[b*x]/x) + (b*SinIntegral[(b^2*Pi*x^2)/2])/2","A",1
11,1,44,44,0.0189581,"\int \frac{S(b x)}{x^3} \, dx","Integrate[FresnelS[b*x]/x^3,x]","\frac{1}{2} \pi  b^2 C(b x)-\frac{b \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{2 x}-\frac{S(b x)}{2 x^2}","\frac{1}{2} \pi  b^2 C(b x)-\frac{b \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{2 x}-\frac{S(b x)}{2 x^2}",1,"(b^2*Pi*FresnelC[b*x])/2 - FresnelS[b*x]/(2*x^2) - (b*Sin[(b^2*Pi*x^2)/2])/(2*x)","A",1
12,1,52,52,0.0196039,"\int \frac{S(b x)}{x^4} \, dx","Integrate[FresnelS[b*x]/x^4,x]","-\frac{b \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 x^2}+\frac{1}{12} \pi  b^3 \text{Ci}\left(\frac{1}{2} b^2 \pi  x^2\right)-\frac{S(b x)}{3 x^3}","-\frac{b \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 x^2}+\frac{1}{12} \pi  b^3 \text{Ci}\left(\frac{1}{2} b^2 \pi  x^2\right)-\frac{S(b x)}{3 x^3}",1,"(b^3*Pi*CosIntegral[(b^2*Pi*x^2)/2])/12 - FresnelS[b*x]/(3*x^3) - (b*Sin[(b^2*Pi*x^2)/2])/(6*x^2)","A",1
13,1,69,69,0.0181328,"\int \frac{S(b x)}{x^5} \, dx","Integrate[FresnelS[b*x]/x^5,x]","-\frac{1}{12} \pi ^2 b^4 S(b x)-\frac{b \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{12 x^3}-\frac{\pi  b^3 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{12 x}-\frac{S(b x)}{4 x^4}","-\frac{1}{12} \pi ^2 b^4 S(b x)-\frac{b \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{12 x^3}-\frac{\pi  b^3 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{12 x}-\frac{S(b x)}{4 x^4}",1,"-1/12*(b^3*Pi*Cos[(b^2*Pi*x^2)/2])/x - (b^4*Pi^2*FresnelS[b*x])/12 - FresnelS[b*x]/(4*x^4) - (b*Sin[(b^2*Pi*x^2)/2])/(12*x^3)","A",1
14,1,77,77,0.0355249,"\int \frac{S(b x)}{x^6} \, dx","Integrate[FresnelS[b*x]/x^6,x]","-\frac{b \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{20 x^4}-\frac{1}{80} \pi ^2 b^5 \text{Si}\left(\frac{1}{2} b^2 \pi  x^2\right)-\frac{\pi  b^3 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{40 x^2}-\frac{S(b x)}{5 x^5}","-\frac{b \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{20 x^4}-\frac{1}{80} \pi ^2 b^5 \text{Si}\left(\frac{1}{2} b^2 \pi  x^2\right)-\frac{\pi  b^3 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{40 x^2}-\frac{S(b x)}{5 x^5}",1,"-1/40*(b^3*Pi*Cos[(b^2*Pi*x^2)/2])/x^2 - FresnelS[b*x]/(5*x^5) - (b*Sin[(b^2*Pi*x^2)/2])/(20*x^4) - (b^5*Pi^2*SinIntegral[(b^2*Pi*x^2)/2])/80","A",1
15,1,76,94,0.064172,"\int \frac{S(b x)}{x^7} \, dx","Integrate[FresnelS[b*x]/x^7,x]","\frac{1}{90} \left(-\pi ^3 b^6 C(b x)+\frac{b \left(\pi ^2 b^4 x^4-3\right) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x^5}-\frac{\pi  b^3 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x^3}-\frac{15 S(b x)}{x^6}\right)","-\frac{1}{90} \pi ^3 b^6 C(b x)-\frac{b \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{30 x^5}+\frac{\pi ^2 b^5 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{90 x}-\frac{\pi  b^3 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{90 x^3}-\frac{S(b x)}{6 x^6}",1,"(-((b^3*Pi*Cos[(b^2*Pi*x^2)/2])/x^3) - b^6*Pi^3*FresnelC[b*x] - (15*FresnelS[b*x])/x^6 + (b*(-3 + b^4*Pi^2*x^4)*Sin[(b^2*Pi*x^2)/2])/x^5)/90","A",1
16,1,85,102,0.0802149,"\int \frac{S(b x)}{x^8} \, dx","Integrate[FresnelS[b*x]/x^8,x]","\frac{1}{672} \left(-\pi ^3 b^7 \text{Ci}\left(\frac{1}{2} b^2 \pi  x^2\right)+\frac{2 b \left(\pi ^2 b^4 x^4-8\right) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x^6}-\frac{4 \pi  b^3 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x^4}-\frac{96 S(b x)}{x^7}\right)","-\frac{b \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{42 x^6}-\frac{1}{672} \pi ^3 b^7 \text{Ci}\left(\frac{1}{2} b^2 \pi  x^2\right)+\frac{\pi ^2 b^5 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{336 x^2}-\frac{\pi  b^3 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{168 x^4}-\frac{S(b x)}{7 x^7}",1,"((-4*b^3*Pi*Cos[(b^2*Pi*x^2)/2])/x^4 - b^7*Pi^3*CosIntegral[(b^2*Pi*x^2)/2] - (96*FresnelS[b*x])/x^7 + (2*b*(-8 + b^4*Pi^2*x^4)*Sin[(b^2*Pi*x^2)/2])/x^6)/672","A",1
17,1,84,119,0.0750942,"\int \frac{S(b x)}{x^9} \, dx","Integrate[FresnelS[b*x]/x^9,x]","\frac{\left(\pi ^4 b^8 x^8-105\right) S(b x)+b x \left(\pi ^2 b^4 x^4-15\right) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)+\pi  b^3 x^3 \left(\pi ^2 b^4 x^4-3\right) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{840 x^8}","\frac{1}{840} \pi ^4 b^8 S(b x)-\frac{b \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{56 x^7}+\frac{\pi ^3 b^7 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{840 x}+\frac{\pi ^2 b^5 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{840 x^3}-\frac{\pi  b^3 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{280 x^5}-\frac{S(b x)}{8 x^8}",1,"(b^3*Pi*x^3*(-3 + b^4*Pi^2*x^4)*Cos[(b^2*Pi*x^2)/2] + (-105 + b^8*Pi^4*x^8)*FresnelS[b*x] + b*x*(-15 + b^4*Pi^2*x^4)*Sin[(b^2*Pi*x^2)/2])/(840*x^8)","A",1
18,1,96,127,0.2075056,"\int \frac{S(b x)}{x^{10}} \, dx","Integrate[FresnelS[b*x]/x^10,x]","\frac{\pi ^4 b^9 \text{Si}\left(\frac{1}{2} b^2 \pi  x^2\right)+\frac{4 b \left(\pi ^2 b^4 x^4-24\right) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x^8}+\frac{2 \pi  b^3 \left(\pi ^2 b^4 x^4-8\right) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x^6}-\frac{768 S(b x)}{x^9}}{6912}","-\frac{b \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{72 x^8}+\frac{\pi ^4 b^9 \text{Si}\left(\frac{1}{2} b^2 \pi  x^2\right)}{6912}+\frac{\pi ^3 b^7 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{3456 x^2}+\frac{\pi ^2 b^5 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{1728 x^4}-\frac{\pi  b^3 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{432 x^6}-\frac{S(b x)}{9 x^9}",1,"((2*b^3*Pi*(-8 + b^4*Pi^2*x^4)*Cos[(b^2*Pi*x^2)/2])/x^6 - (768*FresnelS[b*x])/x^9 + (4*b*(-24 + b^4*Pi^2*x^4)*Sin[(b^2*Pi*x^2)/2])/x^8 + b^9*Pi^4*SinIntegral[(b^2*Pi*x^2)/2])/6912","A",1
19,1,424,296,1.0175312,"\int (c+d x)^3 S(a+b x) \, dx","Integrate[(c + d*x)^3*FresnelS[a + b*x],x]","\frac{-\pi  a^3 d^3 \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)+4 \pi  a^2 b c d^2 \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)+\pi  a^2 b d^3 x \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)+S(a+b x) \left(d^3 \left(-\pi ^2 a^4+\pi ^2 b^4 x^4+3\right)+4 \pi ^2 b c d^2 \left(a^3+b^3 x^3\right)+6 \pi ^2 b^2 c^2 d \left(b^2 x^2-a^2\right)+4 \pi ^2 b^3 c^3 (a+b x)\right)+4 \pi  b^3 c^3 \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)+6 \pi  b^3 c^2 d x \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)+4 \pi  b^3 c d^2 x^2 \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)+\pi  b^3 d^3 x^3 \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)-6 \pi  a b^2 c^2 d \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)-4 \pi  a b^2 c d^2 x \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)-\pi  a b^2 d^3 x^2 \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)-8 b c d^2 \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)-6 \pi  d (b c-a d)^2 C(a+b x)-3 b d^3 x \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)+5 a d^3 \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{4 \pi ^2 b^4}","-\frac{2 d^2 (b c-a d) \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi ^2 b^4}+\frac{d^2 (a+b x)^2 (b c-a d) \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b^4}-\frac{3 d (b c-a d)^2 C(a+b x)}{2 \pi  b^4}-\frac{(b c-a d)^4 S(a+b x)}{4 b^4 d}+\frac{(b c-a d)^3 \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b^4}+\frac{3 d (a+b x) (b c-a d)^2 \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{2 \pi  b^4}+\frac{3 d^3 S(a+b x)}{4 \pi ^2 b^4}-\frac{3 d^3 (a+b x) \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{4 \pi ^2 b^4}+\frac{d^3 (a+b x)^3 \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{4 \pi  b^4}+\frac{(c+d x)^4 S(a+b x)}{4 d}",1,"(4*b^3*c^3*Pi*Cos[(Pi*(a + b*x)^2)/2] - 6*a*b^2*c^2*d*Pi*Cos[(Pi*(a + b*x)^2)/2] + 4*a^2*b*c*d^2*Pi*Cos[(Pi*(a + b*x)^2)/2] - a^3*d^3*Pi*Cos[(Pi*(a + b*x)^2)/2] + 6*b^3*c^2*d*Pi*x*Cos[(Pi*(a + b*x)^2)/2] - 4*a*b^2*c*d^2*Pi*x*Cos[(Pi*(a + b*x)^2)/2] + a^2*b*d^3*Pi*x*Cos[(Pi*(a + b*x)^2)/2] + 4*b^3*c*d^2*Pi*x^2*Cos[(Pi*(a + b*x)^2)/2] - a*b^2*d^3*Pi*x^2*Cos[(Pi*(a + b*x)^2)/2] + b^3*d^3*Pi*x^3*Cos[(Pi*(a + b*x)^2)/2] - 6*d*(b*c - a*d)^2*Pi*FresnelC[a + b*x] + (4*b^3*c^3*Pi^2*(a + b*x) + 6*b^2*c^2*d*Pi^2*(-a^2 + b^2*x^2) + 4*b*c*d^2*Pi^2*(a^3 + b^3*x^3) + d^3*(3 - a^4*Pi^2 + b^4*Pi^2*x^4))*FresnelS[a + b*x] - 8*b*c*d^2*Sin[(Pi*(a + b*x)^2)/2] + 5*a*d^3*Sin[(Pi*(a + b*x)^2)/2] - 3*b*d^3*x*Sin[(Pi*(a + b*x)^2)/2])/(4*b^4*Pi^2)","A",1
20,1,236,193,0.5524604,"\int (c+d x)^2 S(a+b x) \, dx","Integrate[(c + d*x)^2*FresnelS[a + b*x],x]","\frac{\pi  a^2 d^2 \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)+\pi ^2 S(a+b x) \left(a^3 d^2-3 a^2 b c d+3 a b^2 c^2+b^3 x \left(3 c^2+3 c d x+d^2 x^2\right)\right)+3 \pi  b^2 c^2 \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)+3 \pi  b^2 c d x \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)+\pi  b^2 d^2 x^2 \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)+3 \pi  d (a d-b c) C(a+b x)-3 \pi  a b c d \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)-2 d^2 \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)-\pi  a b d^2 x \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{3 \pi ^2 b^3}","-\frac{d (b c-a d) C(a+b x)}{\pi  b^3}-\frac{(b c-a d)^3 S(a+b x)}{3 b^3 d}+\frac{(b c-a d)^2 \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b^3}+\frac{d (a+b x) (b c-a d) \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b^3}-\frac{2 d^2 \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{3 \pi ^2 b^3}+\frac{d^2 (a+b x)^2 \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{3 \pi  b^3}+\frac{(c+d x)^3 S(a+b x)}{3 d}",1,"(3*b^2*c^2*Pi*Cos[(Pi*(a + b*x)^2)/2] - 3*a*b*c*d*Pi*Cos[(Pi*(a + b*x)^2)/2] + a^2*d^2*Pi*Cos[(Pi*(a + b*x)^2)/2] + 3*b^2*c*d*Pi*x*Cos[(Pi*(a + b*x)^2)/2] - a*b*d^2*Pi*x*Cos[(Pi*(a + b*x)^2)/2] + b^2*d^2*Pi*x^2*Cos[(Pi*(a + b*x)^2)/2] + 3*d*(-(b*c) + a*d)*Pi*FresnelC[a + b*x] + Pi^2*(3*a*b^2*c^2 - 3*a^2*b*c*d + a^3*d^2 + b^3*x*(3*c^2 + 3*c*d*x + d^2*x^2))*FresnelS[a + b*x] - 2*d^2*Sin[(Pi*(a + b*x)^2)/2])/(3*b^3*Pi^2)","A",1
21,1,61,121,0.277849,"\int (c+d x) S(a+b x) \, dx","Integrate[(c + d*x)*FresnelS[a + b*x],x]","\frac{(-a d+2 b c+b d x) \left(\pi  (a+b x) S(a+b x)+\cos \left(\frac{1}{2} \pi  (a+b x)^2\right)\right)-d C(a+b x)}{2 \pi  b^2}","-\frac{(b c-a d)^2 S(a+b x)}{2 b^2 d}+\frac{(b c-a d) \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b^2}-\frac{d C(a+b x)}{2 \pi  b^2}+\frac{d (a+b x) \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{2 \pi  b^2}+\frac{(c+d x)^2 S(a+b x)}{2 d}",1,"(-(d*FresnelC[a + b*x]) + (2*b*c - a*d + b*d*x)*(Cos[(Pi*(a + b*x)^2)/2] + Pi*(a + b*x)*FresnelS[a + b*x]))/(2*b^2*Pi)","A",1
22,1,89,36,0.0442036,"\int S(a+b x) \, dx","Integrate[FresnelS[a + b*x],x]","-\frac{\sin \left(\frac{\pi  a^2}{2}\right) \sin \left(\pi  a b x+\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b}+\frac{\cos \left(\frac{\pi  a^2}{2}\right) \cos \left(\pi  a b x+\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b}+x S(a+b x)+\frac{a S(a+b x)}{b}","\frac{(a+b x) S(a+b x)}{b}+\frac{\cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b}",1,"(Cos[(a^2*Pi)/2]*Cos[a*b*Pi*x + (b^2*Pi*x^2)/2])/(b*Pi) + (a*FresnelS[a + b*x])/b + x*FresnelS[a + b*x] - (Sin[(a^2*Pi)/2]*Sin[a*b*Pi*x + (b^2*Pi*x^2)/2])/(b*Pi)","B",1
23,0,0,17,0.0330333,"\int \frac{S(a+b x)}{c+d x} \, dx","Integrate[FresnelS[a + b*x]/(c + d*x),x]","\int \frac{S(a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{S(a+b x)}{c+d x},x\right)",0,"Integrate[FresnelS[a + b*x]/(c + d*x), x]","A",-1
24,0,0,17,5.7831063,"\int \frac{S(a+b x)}{(c+d x)^2} \, dx","Integrate[FresnelS[a + b*x]/(c + d*x)^2,x]","\int \frac{S(a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{S(a+b x)}{(c+d x)^2},x\right)",0,"Integrate[FresnelS[a + b*x]/(c + d*x)^2, x]","A",-1
25,1,166,229,0.3722043,"\int x^3 S(a+b x) \, dx","Integrate[x^3*FresnelS[a + b*x],x]","\frac{\left(-\pi ^2 a^4+\pi ^2 b^4 x^4+3\right) S(a+b x)-\pi  a^3 \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)-6 \pi  a^2 C(a+b x)+\pi  a^2 b x \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)+\pi  b^3 x^3 \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)-\pi  a b^2 x^2 \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)+5 a \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)-3 b x \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{4 \pi ^2 b^4}","-\frac{a^4 S(a+b x)}{4 b^4}-\frac{a^3 \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b^4}-\frac{3 a^2 C(a+b x)}{2 \pi  b^4}+\frac{3 a^2 (a+b x) \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{2 \pi  b^4}+\frac{3 S(a+b x)}{4 \pi ^2 b^4}+\frac{2 a \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi ^2 b^4}-\frac{3 (a+b x) \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{4 \pi ^2 b^4}-\frac{a (a+b x)^2 \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b^4}+\frac{(a+b x)^3 \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{4 \pi  b^4}+\frac{1}{4} x^4 S(a+b x)",1,"(-(a^3*Pi*Cos[(Pi*(a + b*x)^2)/2]) + a^2*b*Pi*x*Cos[(Pi*(a + b*x)^2)/2] - a*b^2*Pi*x^2*Cos[(Pi*(a + b*x)^2)/2] + b^3*Pi*x^3*Cos[(Pi*(a + b*x)^2)/2] - 6*a^2*Pi*FresnelC[a + b*x] + (3 - a^4*Pi^2 + b^4*Pi^2*x^4)*FresnelS[a + b*x] + 5*a*Sin[(Pi*(a + b*x)^2)/2] - 3*b*x*Sin[(Pi*(a + b*x)^2)/2])/(4*b^4*Pi^2)","A",1
26,1,115,147,0.2962117,"\int x^2 S(a+b x) \, dx","Integrate[x^2*FresnelS[a + b*x],x]","\frac{\pi ^2 \left(a^3+b^3 x^3\right) S(a+b x)+\pi  a^2 \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)+\pi  b^2 x^2 \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)+3 \pi  a C(a+b x)-2 \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)-\pi  a b x \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{3 \pi ^2 b^3}","\frac{a^3 S(a+b x)}{3 b^3}+\frac{a^2 \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b^3}+\frac{a C(a+b x)}{\pi  b^3}-\frac{2 \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{3 \pi ^2 b^3}-\frac{a (a+b x) \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b^3}+\frac{(a+b x)^2 \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{3 \pi  b^3}+\frac{1}{3} x^3 S(a+b x)",1,"(a^2*Pi*Cos[(Pi*(a + b*x)^2)/2] - a*b*Pi*x*Cos[(Pi*(a + b*x)^2)/2] + b^2*Pi*x^2*Cos[(Pi*(a + b*x)^2)/2] + 3*a*Pi*FresnelC[a + b*x] + Pi^2*(a^3 + b^3*x^3)*FresnelS[a + b*x] - 2*Sin[(Pi*(a + b*x)^2)/2])/(3*b^3*Pi^2)","A",1
27,1,51,96,0.1870673,"\int x S(a+b x) \, dx","Integrate[x*FresnelS[a + b*x],x]","-\frac{C(a+b x)+(a-b x) \left(\pi  (a+b x) S(a+b x)+\cos \left(\frac{1}{2} \pi  (a+b x)^2\right)\right)}{2 \pi  b^2}","-\frac{a^2 S(a+b x)}{2 b^2}-\frac{C(a+b x)}{2 \pi  b^2}-\frac{a \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b^2}+\frac{(a+b x) \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{2 \pi  b^2}+\frac{1}{2} x^2 S(a+b x)",1,"-1/2*(FresnelC[a + b*x] + (a - b*x)*(Cos[(Pi*(a + b*x)^2)/2] + Pi*(a + b*x)*FresnelS[a + b*x]))/(b^2*Pi)","A",1
28,1,89,36,0.0369084,"\int S(a+b x) \, dx","Integrate[FresnelS[a + b*x],x]","-\frac{\sin \left(\frac{\pi  a^2}{2}\right) \sin \left(\pi  a b x+\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b}+\frac{\cos \left(\frac{\pi  a^2}{2}\right) \cos \left(\pi  a b x+\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b}+x S(a+b x)+\frac{a S(a+b x)}{b}","\frac{(a+b x) S(a+b x)}{b}+\frac{\cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b}",1,"(Cos[(a^2*Pi)/2]*Cos[a*b*Pi*x + (b^2*Pi*x^2)/2])/(b*Pi) + (a*FresnelS[a + b*x])/b + x*FresnelS[a + b*x] - (Sin[(a^2*Pi)/2]*Sin[a*b*Pi*x + (b^2*Pi*x^2)/2])/(b*Pi)","B",1
29,0,0,13,0.0162846,"\int \frac{S(a+b x)}{x} \, dx","Integrate[FresnelS[a + b*x]/x,x]","\int \frac{S(a+b x)}{x} \, dx","\text{Int}\left(\frac{S(a+b x)}{x},x\right)",0,"Integrate[FresnelS[a + b*x]/x, x]","A",-1
30,0,0,13,3.6744822,"\int \frac{S(a+b x)}{x^2} \, dx","Integrate[FresnelS[a + b*x]/x^2,x]","\int \frac{S(a+b x)}{x^2} \, dx","\text{Int}\left(\frac{S(a+b x)}{x^2},x\right)",0,"Integrate[FresnelS[a + b*x]/x^2, x]","A",-1
31,1,253,253,0.0164014,"\int x^7 S(b x)^2 \, dx","Integrate[x^7*FresnelS[b*x]^2,x]","-\frac{105 S(b x)^2}{8 \pi ^4 b^8}-\frac{105 x^2}{16 \pi ^4 b^6}+\frac{x^7 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi  b}+\frac{7 x^6}{48 \pi ^2 b^2}+\frac{x^6 \cos \left(\pi  b^2 x^2\right)}{16 \pi ^2 b^2}+\frac{10 \sin \left(\pi  b^2 x^2\right)}{\pi ^5 b^8}+\frac{105 x S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi ^4 b^7}-\frac{55 x^2 \cos \left(\pi  b^2 x^2\right)}{16 \pi ^4 b^6}-\frac{35 x^3 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi ^3 b^5}-\frac{5 x^4 \sin \left(\pi  b^2 x^2\right)}{8 \pi ^3 b^4}-\frac{7 x^5 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi ^2 b^3}+\frac{1}{8} x^8 S(b x)^2","-\frac{105 S(b x)^2}{8 \pi ^4 b^8}-\frac{105 x^2}{16 \pi ^4 b^6}+\frac{x^7 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi  b}+\frac{7 x^6}{48 \pi ^2 b^2}+\frac{x^6 \cos \left(\pi  b^2 x^2\right)}{16 \pi ^2 b^2}+\frac{10 \sin \left(\pi  b^2 x^2\right)}{\pi ^5 b^8}+\frac{105 x S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi ^4 b^7}-\frac{55 x^2 \cos \left(\pi  b^2 x^2\right)}{16 \pi ^4 b^6}-\frac{35 x^3 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi ^3 b^5}-\frac{5 x^4 \sin \left(\pi  b^2 x^2\right)}{8 \pi ^3 b^4}-\frac{7 x^5 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi ^2 b^3}+\frac{1}{8} x^8 S(b x)^2",1,"(-105*x^2)/(16*b^6*Pi^4) + (7*x^6)/(48*b^2*Pi^2) - (55*x^2*Cos[b^2*Pi*x^2])/(16*b^6*Pi^4) + (x^6*Cos[b^2*Pi*x^2])/(16*b^2*Pi^2) - (35*x^3*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(4*b^5*Pi^3) + (x^7*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(4*b*Pi) - (105*FresnelS[b*x]^2)/(8*b^8*Pi^4) + (x^8*FresnelS[b*x]^2)/8 + (105*x*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(4*b^7*Pi^4) - (7*x^5*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(4*b^3*Pi^2) + (10*Sin[b^2*Pi*x^2])/(b^8*Pi^5) - (5*x^4*Sin[b^2*Pi*x^2])/(8*b^4*Pi^3)","A",1
32,1,171,239,0.3276869,"\int x^6 S(b x)^2 \, dx","Integrate[x^6*FresnelS[b*x]^2,x]","\frac{80 \pi ^4 b^7 x^7 S(b x)^2+160 S(b x) \left(\pi  b^2 x^2 \left(\pi ^2 b^4 x^4-24\right) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)-6 \left(\pi ^2 b^4 x^4-8\right) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)\right)+2 b x \left(5 \left(4 \pi ^2 b^4 x^4-147\right) \cos \left(\pi  b^2 x^2\right)-2 \left(-24 \pi ^2 b^4 x^4+85 \pi  b^2 x^2 \sin \left(\pi  b^2 x^2\right)+960\right)\right)+2655 \sqrt{2} C\left(\sqrt{2} b x\right)}{560 \pi ^4 b^7}","\frac{531 C\left(\sqrt{2} b x\right)}{56 \sqrt{2} \pi ^4 b^7}-\frac{48 x}{7 \pi ^4 b^6}+\frac{2 x^6 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi  b}+\frac{6 x^5}{35 \pi ^2 b^2}+\frac{x^5 \cos \left(\pi  b^2 x^2\right)}{14 \pi ^2 b^2}+\frac{96 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi ^4 b^7}-\frac{21 x \cos \left(\pi  b^2 x^2\right)}{8 \pi ^4 b^6}-\frac{48 x^2 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi ^3 b^5}-\frac{17 x^3 \sin \left(\pi  b^2 x^2\right)}{28 \pi ^3 b^4}-\frac{12 x^4 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi ^2 b^3}+\frac{1}{7} x^7 S(b x)^2",1,"(2655*Sqrt[2]*FresnelC[Sqrt[2]*b*x] + 80*b^7*Pi^4*x^7*FresnelS[b*x]^2 + 160*FresnelS[b*x]*(b^2*Pi*x^2*(-24 + b^4*Pi^2*x^4)*Cos[(b^2*Pi*x^2)/2] - 6*(-8 + b^4*Pi^2*x^4)*Sin[(b^2*Pi*x^2)/2]) + 2*b*x*(5*(-147 + 4*b^4*Pi^2*x^4)*Cos[b^2*Pi*x^2] - 2*(960 - 24*b^4*Pi^2*x^4 + 85*b^2*Pi*x^2*Sin[b^2*Pi*x^2])))/(560*b^7*Pi^4)","A",1
33,0,0,265,0.257517,"\int x^5 S(b x)^2 \, dx","Integrate[x^5*FresnelS[b*x]^2,x]","\int x^5 S(b x)^2 \, dx","-\frac{5 i x^2 \, _2F_2\left(1,1;\frac{3}{2},2;-\frac{1}{2} i b^2 \pi  x^2\right)}{8 \pi ^3 b^4}+\frac{5 i x^2 \, _2F_2\left(1,1;\frac{3}{2},2;\frac{1}{2} i b^2 \pi  x^2\right)}{8 \pi ^3 b^4}+\frac{5 C(b x) S(b x)}{2 \pi ^3 b^6}+\frac{x^5 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 \pi  b}+\frac{5 x^4}{24 \pi ^2 b^2}+\frac{x^4 \cos \left(\pi  b^2 x^2\right)}{12 \pi ^2 b^2}-\frac{11 \cos \left(\pi  b^2 x^2\right)}{6 \pi ^4 b^6}-\frac{5 x S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^5}-\frac{7 x^2 \sin \left(\pi  b^2 x^2\right)}{12 \pi ^3 b^4}-\frac{5 x^3 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 \pi ^2 b^3}+\frac{1}{6} x^6 S(b x)^2",1,"Integrate[x^5*FresnelS[b*x]^2, x]","F",-1
34,1,137,177,0.1717047,"\int x^4 S(b x)^2 \, dx","Integrate[x^4*FresnelS[b*x]^2,x]","\frac{24 \pi ^3 b^5 x^5 S(b x)^2+32 \pi  b^3 x^3-66 b x \sin \left(\pi  b^2 x^2\right)+48 S(b x) \left(\left(\pi ^2 b^4 x^4-8\right) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)-4 \pi  b^2 x^2 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)\right)+12 \pi  b^3 x^3 \cos \left(\pi  b^2 x^2\right)+129 \sqrt{2} S\left(\sqrt{2} b x\right)}{120 \pi ^3 b^5}","\frac{43 S\left(\sqrt{2} b x\right)}{20 \sqrt{2} \pi ^3 b^5}+\frac{2 x^4 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 \pi  b}+\frac{4 x^3}{15 \pi ^2 b^2}+\frac{x^3 \cos \left(\pi  b^2 x^2\right)}{10 \pi ^2 b^2}-\frac{16 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 \pi ^3 b^5}-\frac{11 x \sin \left(\pi  b^2 x^2\right)}{20 \pi ^3 b^4}-\frac{8 x^2 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 \pi ^2 b^3}+\frac{1}{5} x^5 S(b x)^2",1,"(32*b^3*Pi*x^3 + 12*b^3*Pi*x^3*Cos[b^2*Pi*x^2] + 24*b^5*Pi^3*x^5*FresnelS[b*x]^2 + 129*Sqrt[2]*FresnelS[Sqrt[2]*b*x] + 48*FresnelS[b*x]*((-8 + b^4*Pi^2*x^4)*Cos[(b^2*Pi*x^2)/2] - 4*b^2*Pi*x^2*Sin[(b^2*Pi*x^2)/2]) - 66*b*x*Sin[b^2*Pi*x^2])/(120*b^5*Pi^3)","A",1
35,1,140,140,0.0064115,"\int x^3 S(b x)^2 \, dx","Integrate[x^3*FresnelS[b*x]^2,x]","\frac{3 S(b x)^2}{4 \pi ^2 b^4}+\frac{x^3 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{2 \pi  b}+\frac{3 x^2}{8 \pi ^2 b^2}+\frac{x^2 \cos \left(\pi  b^2 x^2\right)}{8 \pi ^2 b^2}-\frac{\sin \left(\pi  b^2 x^2\right)}{2 \pi ^3 b^4}-\frac{3 x S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{2 \pi ^2 b^3}+\frac{1}{4} x^4 S(b x)^2","\frac{3 S(b x)^2}{4 \pi ^2 b^4}+\frac{x^3 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{2 \pi  b}+\frac{3 x^2}{8 \pi ^2 b^2}+\frac{x^2 \cos \left(\pi  b^2 x^2\right)}{8 \pi ^2 b^2}-\frac{\sin \left(\pi  b^2 x^2\right)}{2 \pi ^3 b^4}-\frac{3 x S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{2 \pi ^2 b^3}+\frac{1}{4} x^4 S(b x)^2",1,"(3*x^2)/(8*b^2*Pi^2) + (x^2*Cos[b^2*Pi*x^2])/(8*b^2*Pi^2) + (x^3*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(2*b*Pi) + (3*FresnelS[b*x]^2)/(4*b^4*Pi^2) + (x^4*FresnelS[b*x]^2)/4 - (3*x*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(2*b^3*Pi^2) - Sin[b^2*Pi*x^2]/(2*b^4*Pi^3)","A",1
36,1,100,124,0.1315891,"\int x^2 S(b x)^2 \, dx","Integrate[x^2*FresnelS[b*x]^2,x]","\frac{4 \pi ^2 b^3 x^3 S(b x)^2+8 S(b x) \left(\pi  b^2 x^2 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)-2 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)\right)+2 b x \left(\cos \left(\pi  b^2 x^2\right)+4\right)-5 \sqrt{2} C\left(\sqrt{2} b x\right)}{12 \pi ^2 b^3}","-\frac{5 C\left(\sqrt{2} b x\right)}{6 \sqrt{2} \pi ^2 b^3}+\frac{2 x^2 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 \pi  b}+\frac{x \cos \left(\pi  b^2 x^2\right)}{6 \pi ^2 b^2}+\frac{2 x}{3 \pi ^2 b^2}-\frac{4 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 \pi ^2 b^3}+\frac{1}{3} x^3 S(b x)^2",1,"(2*b*x*(4 + Cos[b^2*Pi*x^2]) - 5*Sqrt[2]*FresnelC[Sqrt[2]*b*x] + 4*b^3*Pi^2*x^3*FresnelS[b*x]^2 + 8*FresnelS[b*x]*(b^2*Pi*x^2*Cos[(b^2*Pi*x^2)/2] - 2*Sin[(b^2*Pi*x^2)/2]))/(12*b^3*Pi^2)","A",1
37,0,0,143,0.1948803,"\int x S(b x)^2 \, dx","Integrate[x*FresnelS[b*x]^2,x]","\int x S(b x)^2 \, dx","\frac{i x^2 \, _2F_2\left(1,1;\frac{3}{2},2;-\frac{1}{2} i b^2 \pi  x^2\right)}{8 \pi }-\frac{i x^2 \, _2F_2\left(1,1;\frac{3}{2},2;\frac{1}{2} i b^2 \pi  x^2\right)}{8 \pi }-\frac{C(b x) S(b x)}{2 \pi  b^2}+\frac{x S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b}+\frac{\cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^2}+\frac{1}{2} x^2 S(b x)^2",1,"Integrate[x*FresnelS[b*x]^2, x]","F",-1
38,1,55,55,0.0157855,"\int S(b x)^2 \, dx","Integrate[FresnelS[b*x]^2,x]","\frac{2 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b}+x S(b x)^2-\frac{S\left(\sqrt{2} b x\right)}{\sqrt{2} \pi  b}","\frac{2 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b}+x S(b x)^2-\frac{S\left(\sqrt{2} b x\right)}{\sqrt{2} \pi  b}",1,"(2*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(b*Pi) + x*FresnelS[b*x]^2 - FresnelS[Sqrt[2]*b*x]/(Sqrt[2]*b*Pi)","A",1
39,0,0,13,0.0211313,"\int \frac{S(b x)^2}{x} \, dx","Integrate[FresnelS[b*x]^2/x,x]","\int \frac{S(b x)^2}{x} \, dx","\text{Int}\left(\frac{S(b x)^2}{x},x\right)",0,"Integrate[FresnelS[b*x]^2/x, x]","A",-1
40,0,0,38,0.0296339,"\int \frac{S(b x)^2}{x^2} \, dx","Integrate[FresnelS[b*x]^2/x^2,x]","\int \frac{S(b x)^2}{x^2} \, dx","2 b \text{Int}\left(\frac{S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)-\frac{S(b x)^2}{x}",0,"Integrate[FresnelS[b*x]^2/x^2, x]","A",-1
41,0,0,39,0.0221734,"\int \frac{S(b x)^2}{x^3} \, dx","Integrate[FresnelS[b*x]^2/x^3,x]","\int \frac{S(b x)^2}{x^3} \, dx","b \text{Int}\left(\frac{S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x^2},x\right)-\frac{S(b x)^2}{2 x^2}",0,"Integrate[FresnelS[b*x]^2/x^3, x]","A",-1
42,0,0,120,0.031703,"\int \frac{S(b x)^2}{x^4} \, dx","Integrate[FresnelS[b*x]^2/x^4,x]","\int \frac{S(b x)^2}{x^4} \, dx","\frac{1}{3} \pi  b^3 \text{Int}\left(\frac{S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)+\frac{\pi  b^3 S\left(\sqrt{2} b x\right)}{3 \sqrt{2}}-\frac{b S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 x^2}+\frac{b^2 \cos \left(\pi  b^2 x^2\right)}{6 x}-\frac{b^2}{6 x}-\frac{S(b x)^2}{3 x^3}",0,"Integrate[FresnelS[b*x]^2/x^4, x]","A",-1
43,1,127,127,0.0070651,"\int \frac{S(b x)^2}{x^5} \, dx","Integrate[FresnelS[b*x]^2/x^5,x]","-\frac{1}{12} \pi ^2 b^4 S(b x)^2-\frac{b S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 x^3}-\frac{b^2}{24 x^2}+\frac{b^2 \cos \left(\pi  b^2 x^2\right)}{24 x^2}+\frac{1}{12} \pi  b^4 \text{Si}\left(b^2 \pi  x^2\right)-\frac{\pi  b^3 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 x}-\frac{S(b x)^2}{4 x^4}","-\frac{1}{12} \pi ^2 b^4 S(b x)^2-\frac{b S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 x^3}-\frac{b^2}{24 x^2}+\frac{b^2 \cos \left(\pi  b^2 x^2\right)}{24 x^2}+\frac{1}{12} \pi  b^4 \text{Si}\left(b^2 \pi  x^2\right)-\frac{\pi  b^3 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 x}-\frac{S(b x)^2}{4 x^4}",1,"-1/24*b^2/x^2 + (b^2*Cos[b^2*Pi*x^2])/(24*x^2) - (b^3*Pi*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(6*x) - (b^4*Pi^2*FresnelS[b*x]^2)/12 - FresnelS[b*x]^2/(4*x^4) - (b*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(6*x^3) + (b^4*Pi*SinIntegral[b^2*Pi*x^2])/12","A",1
44,0,0,171,0.0349328,"\int \frac{S(b x)^2}{x^6} \, dx","Integrate[FresnelS[b*x]^2/x^6,x]","\int \frac{S(b x)^2}{x^6} \, dx","-\frac{1}{20} \pi ^2 b^5 \text{Int}\left(\frac{S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)+\frac{7 \pi ^2 b^5 C\left(\sqrt{2} b x\right)}{60 \sqrt{2}}-\frac{b S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{10 x^4}-\frac{b^2}{60 x^3}+\frac{b^2 \cos \left(\pi  b^2 x^2\right)}{60 x^3}-\frac{7 \pi  b^4 \sin \left(\pi  b^2 x^2\right)}{120 x}-\frac{\pi  b^3 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{20 x^2}-\frac{S(b x)^2}{5 x^5}",0,"Integrate[FresnelS[b*x]^2/x^6, x]","A",-1
45,0,0,166,0.0273848,"\int \frac{S(b x)^2}{x^7} \, dx","Integrate[FresnelS[b*x]^2/x^7,x]","\int \frac{S(b x)^2}{x^7} \, dx","-\frac{1}{45} \pi ^2 b^5 \text{Int}\left(\frac{S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x^2},x\right)-\frac{b S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{15 x^5}-\frac{b^2}{120 x^4}+\frac{b^2 \cos \left(\pi  b^2 x^2\right)}{120 x^4}+\frac{1}{72} \pi ^2 b^6 \text{Ci}\left(b^2 \pi  x^2\right)-\frac{\pi  b^4 \sin \left(\pi  b^2 x^2\right)}{72 x^2}-\frac{\pi  b^3 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{45 x^3}-\frac{S(b x)^2}{6 x^6}",0,"Integrate[FresnelS[b*x]^2/x^7, x]","A",-1
46,0,0,259,0.0350425,"\int \frac{S(b x)^2}{x^8} \, dx","Integrate[FresnelS[b*x]^2/x^8,x]","\int \frac{S(b x)^2}{x^8} \, dx","-\frac{1}{168} \pi ^3 b^7 \text{Int}\left(\frac{S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)-\frac{2}{315} \sqrt{2} \pi ^3 b^7 S\left(\sqrt{2} b x\right)-\frac{\pi ^3 b^7 S\left(\sqrt{2} b x\right)}{72 \sqrt{2}}+\frac{\pi ^2 b^6}{336 x}-\frac{b S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{21 x^6}-\frac{b^2}{210 x^5}+\frac{b^2 \cos \left(\pi  b^2 x^2\right)}{210 x^5}-\frac{67 \pi ^2 b^6 \cos \left(\pi  b^2 x^2\right)}{5040 x}+\frac{\pi ^2 b^5 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{168 x^2}-\frac{13 \pi  b^4 \sin \left(\pi  b^2 x^2\right)}{2520 x^3}-\frac{\pi  b^3 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{84 x^4}-\frac{S(b x)^2}{7 x^7}",0,"Integrate[FresnelS[b*x]^2/x^8, x]","A",-1
47,1,242,242,0.0166176,"\int \frac{S(b x)^2}{x^9} \, dx","Integrate[FresnelS[b*x]^2/x^9,x]","\frac{1}{840} \pi ^4 b^8 S(b x)^2+\frac{\pi ^2 b^6}{1680 x^2}-\frac{b S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{28 x^7}-\frac{b^2}{336 x^6}+\frac{b^2 \cos \left(\pi  b^2 x^2\right)}{336 x^6}-\frac{1}{280} \pi ^3 b^8 \text{Si}\left(b^2 \pi  x^2\right)+\frac{\pi ^3 b^7 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{420 x}-\frac{\pi ^2 b^6 \cos \left(\pi  b^2 x^2\right)}{336 x^2}+\frac{\pi ^2 b^5 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{420 x^3}-\frac{\pi  b^4 \sin \left(\pi  b^2 x^2\right)}{420 x^4}-\frac{\pi  b^3 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{140 x^5}-\frac{S(b x)^2}{8 x^8}","\frac{1}{840} \pi ^4 b^8 S(b x)^2+\frac{\pi ^2 b^6}{1680 x^2}-\frac{b S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{28 x^7}-\frac{b^2}{336 x^6}+\frac{b^2 \cos \left(\pi  b^2 x^2\right)}{336 x^6}-\frac{1}{280} \pi ^3 b^8 \text{Si}\left(b^2 \pi  x^2\right)+\frac{\pi ^3 b^7 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{420 x}-\frac{\pi ^2 b^6 \cos \left(\pi  b^2 x^2\right)}{336 x^2}+\frac{\pi ^2 b^5 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{420 x^3}-\frac{\pi  b^4 \sin \left(\pi  b^2 x^2\right)}{420 x^4}-\frac{\pi  b^3 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{140 x^5}-\frac{S(b x)^2}{8 x^8}",1,"-1/336*b^2/x^6 + (b^6*Pi^2)/(1680*x^2) + (b^2*Cos[b^2*Pi*x^2])/(336*x^6) - (b^6*Pi^2*Cos[b^2*Pi*x^2])/(336*x^2) - (b^3*Pi*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(140*x^5) + (b^7*Pi^3*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(420*x) + (b^8*Pi^4*FresnelS[b*x]^2)/840 - FresnelS[b*x]^2/(8*x^8) - (b*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(28*x^7) + (b^5*Pi^2*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(420*x^3) - (b^4*Pi*Sin[b^2*Pi*x^2])/(420*x^4) - (b^8*Pi^3*SinIntegral[b^2*Pi*x^2])/280","A",1
48,0,0,286,0.0278276,"\int \frac{S(b x)^2}{x^{10}} \, dx","Integrate[FresnelS[b*x]^2/x^10,x]","\int \frac{S(b x)^2}{x^{10}} \, dx","\frac{\pi ^4 b^9 \text{Int}\left(\frac{S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)}{1728}-\frac{853 \pi ^4 b^9 C\left(\sqrt{2} b x\right)}{181440 \sqrt{2}}+\frac{\pi ^2 b^6}{5184 x^3}-\frac{b S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{36 x^8}-\frac{b^2}{504 x^7}+\frac{b^2 \cos \left(\pi  b^2 x^2\right)}{504 x^7}+\frac{853 \pi ^3 b^8 \sin \left(\pi  b^2 x^2\right)}{362880 x}+\frac{\pi ^3 b^7 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{1728 x^2}-\frac{187 \pi ^2 b^6 \cos \left(\pi  b^2 x^2\right)}{181440 x^3}+\frac{\pi ^2 b^5 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{864 x^4}-\frac{19 \pi  b^4 \sin \left(\pi  b^2 x^2\right)}{15120 x^5}-\frac{\pi  b^3 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{216 x^6}-\frac{S(b x)^2}{9 x^9}",0,"Integrate[FresnelS[b*x]^2/x^10, x]","A",-1
49,0,0,497,0.8805792,"\int (c+d x)^2 S(a+b x)^2 \, dx","Integrate[(c + d*x)^2*FresnelS[a + b*x]^2,x]","\int (c+d x)^2 S(a+b x)^2 \, dx","\frac{i d (a+b x)^2 (b c-a d) \, _2F_2\left(1,1;\frac{3}{2},2;-\frac{1}{2} i \pi  (a+b x)^2\right)}{4 \pi  b^3}-\frac{i d (a+b x)^2 (b c-a d) \, _2F_2\left(1,1;\frac{3}{2},2;\frac{1}{2} i \pi  (a+b x)^2\right)}{4 \pi  b^3}-\frac{d (b c-a d) C(a+b x) S(a+b x)}{\pi  b^3}+\frac{d (a+b x)^2 (b c-a d) S(a+b x)^2}{b^3}+\frac{(a+b x) (b c-a d)^2 S(a+b x)^2}{b^3}-\frac{(b c-a d)^2 S\left(\sqrt{2} (a+b x)\right)}{\sqrt{2} \pi  b^3}+\frac{2 d (a+b x) (b c-a d) S(a+b x) \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b^3}+\frac{2 (b c-a d)^2 S(a+b x) \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b^3}+\frac{d (b c-a d) \cos \left(\pi  (a+b x)^2\right)}{2 \pi ^2 b^3}-\frac{5 d^2 C\left(\sqrt{2} (a+b x)\right)}{6 \sqrt{2} \pi ^2 b^3}+\frac{d^2 (a+b x)^3 S(a+b x)^2}{3 b^3}-\frac{4 d^2 S(a+b x) \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{3 \pi ^2 b^3}+\frac{2 d^2 (a+b x)^2 S(a+b x) \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{3 \pi  b^3}+\frac{d^2 (a+b x) \cos \left(\pi  (a+b x)^2\right)}{6 \pi ^2 b^3}+\frac{2 d^2 x}{3 \pi ^2 b^2}",1,"Integrate[(c + d*x)^2*FresnelS[a + b*x]^2, x]","F",-1
50,0,0,279,0.6187237,"\int (c+d x) S(a+b x)^2 \, dx","Integrate[(c + d*x)*FresnelS[a + b*x]^2,x]","\int (c+d x) S(a+b x)^2 \, dx","\frac{i d (a+b x)^2 \, _2F_2\left(1,1;\frac{3}{2},2;-\frac{1}{2} i \pi  (a+b x)^2\right)}{8 \pi  b^2}-\frac{i d (a+b x)^2 \, _2F_2\left(1,1;\frac{3}{2},2;\frac{1}{2} i \pi  (a+b x)^2\right)}{8 \pi  b^2}+\frac{(a+b x) (b c-a d) S(a+b x)^2}{b^2}-\frac{(b c-a d) S\left(\sqrt{2} (a+b x)\right)}{\sqrt{2} \pi  b^2}+\frac{2 (b c-a d) S(a+b x) \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b^2}-\frac{d C(a+b x) S(a+b x)}{2 \pi  b^2}+\frac{d (a+b x)^2 S(a+b x)^2}{2 b^2}+\frac{d (a+b x) S(a+b x) \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b^2}+\frac{d \cos \left(\pi  (a+b x)^2\right)}{4 \pi ^2 b^2}",1,"Integrate[(c + d*x)*FresnelS[a + b*x]^2, x]","F",-1
51,1,67,70,0.0113654,"\int S(a+b x)^2 \, dx","Integrate[FresnelS[a + b*x]^2,x]","\frac{2 \pi  (a+b x) S(a+b x)^2-\sqrt{2} S\left(\sqrt{2} (a+b x)\right)+4 S(a+b x) \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{2 \pi  b}","\frac{(a+b x) S(a+b x)^2}{b}-\frac{S\left(\sqrt{2} (a+b x)\right)}{\sqrt{2} \pi  b}+\frac{2 S(a+b x) \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b}",1,"(4*Cos[(Pi*(a + b*x)^2)/2]*FresnelS[a + b*x] + 2*Pi*(a + b*x)*FresnelS[a + b*x]^2 - Sqrt[2]*FresnelS[Sqrt[2]*(a + b*x)])/(2*b*Pi)","A",1
52,0,0,19,0.0430861,"\int \frac{S(a+b x)^2}{c+d x} \, dx","Integrate[FresnelS[a + b*x]^2/(c + d*x),x]","\int \frac{S(a+b x)^2}{c+d x} \, dx","\text{Int}\left(\frac{S(a+b x)^2}{c+d x},x\right)",0,"Integrate[FresnelS[a + b*x]^2/(c + d*x), x]","A",-1
53,0,0,19,0.0943997,"\int \frac{S(a+b x)^2}{(c+d x)^2} \, dx","Integrate[FresnelS[a + b*x]^2/(c + d*x)^2,x]","\int \frac{S(a+b x)^2}{(c+d x)^2} \, dx","\text{Int}\left(\frac{S(a+b x)^2}{(c+d x)^2},x\right)",0,"Integrate[FresnelS[a + b*x]^2/(c + d*x)^2, x]","A",-1
54,1,319,231,8.3016989,"\int x^2 S\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[x^2*FresnelS[d*(a + b*Log[c*x^n])],x]","\frac{1}{12} x^3 \left(4 S\left(d \left(a+b \log \left(c x^n\right)\right)\right)+\sqrt[4]{-1} \sqrt{2} \left(c x^n\right)^{-3/n} \left(e^{\frac{9 i}{\pi  b^2 d^2 n^2}} \text{erfi}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(\pi  a b d^2 n+\pi  b^2 d^2 n \log \left(c x^n\right)-3 i\right)}{\sqrt{\pi } b d n}\right)+i \text{erfi}\left(\frac{(-1)^{3/4} \left(\pi  a b d^2 n+\pi  b^2 d^2 n \log \left(c x^n\right)+3 i\right)}{\sqrt{2 \pi } b d n}\right)\right) \exp \left(\frac{1}{2} \left(-i \pi  a^2 d^2+2 i \pi  a b d^2 \left(n \log (x)-\log \left(c x^n\right)\right)-\frac{6 a}{b n}-i \pi  b^2 d^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2-\frac{9 i}{\pi  b^2 d^2 n^2}\right)\right) \left(\cos \left(\frac{1}{2} \pi  d^2 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)^2\right)+i \sin \left(\frac{1}{2} \pi  d^2 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)^2\right)\right)\right)","\left(\frac{1}{12}-\frac{i}{12}\right) x^3 \left(c x^n\right)^{-3/n} e^{-\frac{3 a}{b n}+\frac{9 i}{2 \pi  b^2 d^2 n^2}} \text{erf}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(i \pi  a b d^2+i \pi  b^2 d^2 \log \left(c x^n\right)+\frac{3}{n}\right)}{\sqrt{\pi } b d}\right)+\left(\frac{1}{12}-\frac{i}{12}\right) x^3 \left(c x^n\right)^{-3/n} e^{-\frac{3 a}{b n}-\frac{9 i}{2 \pi  b^2 d^2 n^2}} \text{erfi}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(-i \pi  a b d^2-i \pi  b^2 d^2 \log \left(c x^n\right)+\frac{3}{n}\right)}{\sqrt{\pi } b d}\right)+\frac{1}{3} x^3 S\left(d \left(a+b \log \left(c x^n\right)\right)\right)",1,"(x^3*(4*FresnelS[d*(a + b*Log[c*x^n])] + ((-1)^(1/4)*Sqrt[2]*E^(((-6*a)/(b*n) - (9*I)/(b^2*d^2*n^2*Pi) - I*a^2*d^2*Pi + (2*I)*a*b*d^2*Pi*(n*Log[x] - Log[c*x^n]) - I*b^2*d^2*Pi*(-(n*Log[x]) + Log[c*x^n])^2)/2)*(E^((9*I)/(b^2*d^2*n^2*Pi))*Erfi[((1/2 + I/2)*(-3*I + a*b*d^2*n*Pi + b^2*d^2*n*Pi*Log[c*x^n]))/(b*d*n*Sqrt[Pi])] + I*Erfi[((-1)^(3/4)*(3*I + a*b*d^2*n*Pi + b^2*d^2*n*Pi*Log[c*x^n]))/(b*d*n*Sqrt[2*Pi])])*(Cos[(d^2*Pi*(a - b*n*Log[x] + b*Log[c*x^n])^2)/2] + I*Sin[(d^2*Pi*(a - b*n*Log[x] + b*Log[c*x^n])^2)/2]))/(c*x^n)^(3/n)))/12","A",0
55,1,319,227,7.91171,"\int x S\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[x*FresnelS[d*(a + b*Log[c*x^n])],x]","\frac{1}{8} x^2 \left(4 S\left(d \left(a+b \log \left(c x^n\right)\right)\right)+\sqrt[4]{-1} \sqrt{2} \left(c x^n\right)^{-2/n} \left(e^{\frac{4 i}{\pi  b^2 d^2 n^2}} \text{erfi}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(\pi  a b d^2 n+\pi  b^2 d^2 n \log \left(c x^n\right)-2 i\right)}{\sqrt{\pi } b d n}\right)+i \text{erfi}\left(\frac{(-1)^{3/4} \left(\pi  a b d^2 n+\pi  b^2 d^2 n \log \left(c x^n\right)+2 i\right)}{\sqrt{2 \pi } b d n}\right)\right) \exp \left(-\frac{1}{2} i \pi  a^2 d^2+i \pi  a b d^2 \left(n \log (x)-\log \left(c x^n\right)\right)-\frac{2 a}{b n}-\frac{1}{2} i \pi  b^2 d^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2-\frac{2 i}{\pi  b^2 d^2 n^2}\right) \left(\cos \left(\frac{1}{2} \pi  d^2 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)^2\right)+i \sin \left(\frac{1}{2} \pi  d^2 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)^2\right)\right)\right)","\left(\frac{1}{8}-\frac{i}{8}\right) x^2 \left(c x^n\right)^{-2/n} e^{\frac{-2 \pi  a b d^2 n+2 i}{\pi  b^2 d^2 n^2}} \text{erf}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(i \pi  a b d^2+i \pi  b^2 d^2 \log \left(c x^n\right)+\frac{2}{n}\right)}{\sqrt{\pi } b d}\right)+\left(\frac{1}{8}-\frac{i}{8}\right) x^2 \left(c x^n\right)^{-2/n} e^{-\frac{2 \left(\pi  a b d^2 n+i\right)}{\pi  b^2 d^2 n^2}} \text{erfi}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(-i \pi  a b d^2-i \pi  b^2 d^2 \log \left(c x^n\right)+\frac{2}{n}\right)}{\sqrt{\pi } b d}\right)+\frac{1}{2} x^2 S\left(d \left(a+b \log \left(c x^n\right)\right)\right)",1,"(x^2*(4*FresnelS[d*(a + b*Log[c*x^n])] + ((-1)^(1/4)*Sqrt[2]*E^((-2*a)/(b*n) - (2*I)/(b^2*d^2*n^2*Pi) - (I/2)*a^2*d^2*Pi + I*a*b*d^2*Pi*(n*Log[x] - Log[c*x^n]) - (I/2)*b^2*d^2*Pi*(-(n*Log[x]) + Log[c*x^n])^2)*(E^((4*I)/(b^2*d^2*n^2*Pi))*Erfi[((1/2 + I/2)*(-2*I + a*b*d^2*n*Pi + b^2*d^2*n*Pi*Log[c*x^n]))/(b*d*n*Sqrt[Pi])] + I*Erfi[((-1)^(3/4)*(2*I + a*b*d^2*n*Pi + b^2*d^2*n*Pi*Log[c*x^n]))/(b*d*n*Sqrt[2*Pi])])*(Cos[(d^2*Pi*(a - b*n*Log[x] + b*Log[c*x^n])^2)/2] + I*Sin[(d^2*Pi*(a - b*n*Log[x] + b*Log[c*x^n])^2)/2]))/(c*x^n)^(2/n)))/8","A",0
56,1,316,214,7.7199726,"\int S\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[FresnelS[d*(a + b*Log[c*x^n])],x]","x S\left(d \left(a+b \log \left(c x^n\right)\right)\right)+\frac{\sqrt[4]{-1} x \left(c x^n\right)^{-1/n} \left(e^{\frac{i}{\pi  b^2 d^2 n^2}} \text{erfi}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(\pi  a b d^2 n+\pi  b^2 d^2 n \log \left(c x^n\right)-i\right)}{\sqrt{\pi } b d n}\right)+i \text{erfi}\left(\frac{(-1)^{3/4} \left(\pi  a b d^2 n+\pi  b^2 d^2 n \log \left(c x^n\right)+i\right)}{\sqrt{2 \pi } b d n}\right)\right) \exp \left(\frac{1}{2} \left(-i \pi  a^2 d^2+2 i \pi  a b d^2 \left(n \log (x)-\log \left(c x^n\right)\right)-\frac{2 a}{b n}-i \pi  b^2 d^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2-\frac{i}{\pi  b^2 d^2 n^2}\right)\right) \left(\cos \left(\frac{1}{2} \pi  d^2 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)^2\right)+i \sin \left(\frac{1}{2} \pi  d^2 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)^2\right)\right)}{2 \sqrt{2}}","\left(\frac{1}{4}-\frac{i}{4}\right) x \left(c x^n\right)^{-1/n} e^{-\frac{2 a b n-\frac{i}{\pi  d^2}}{2 b^2 n^2}} \text{erf}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(i \pi  a b d^2+i \pi  b^2 d^2 \log \left(c x^n\right)+\frac{1}{n}\right)}{\sqrt{\pi } b d}\right)+\left(\frac{1}{4}-\frac{i}{4}\right) x \left(c x^n\right)^{-1/n} e^{-\frac{2 a b n+\frac{i}{\pi  d^2}}{2 b^2 n^2}} \text{erfi}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(-i \pi  a b d^2-i \pi  b^2 d^2 \log \left(c x^n\right)+\frac{1}{n}\right)}{\sqrt{\pi } b d}\right)+x S\left(d \left(a+b \log \left(c x^n\right)\right)\right)",1,"x*FresnelS[d*(a + b*Log[c*x^n])] + ((-1)^(1/4)*E^(((-2*a)/(b*n) - I/(b^2*d^2*n^2*Pi) - I*a^2*d^2*Pi + (2*I)*a*b*d^2*Pi*(n*Log[x] - Log[c*x^n]) - I*b^2*d^2*Pi*(-(n*Log[x]) + Log[c*x^n])^2)/2)*x*(E^(I/(b^2*d^2*n^2*Pi))*Erfi[((1/2 + I/2)*(-I + a*b*d^2*n*Pi + b^2*d^2*n*Pi*Log[c*x^n]))/(b*d*n*Sqrt[Pi])] + I*Erfi[((-1)^(3/4)*(I + a*b*d^2*n*Pi + b^2*d^2*n*Pi*Log[c*x^n]))/(b*d*n*Sqrt[2*Pi])])*(Cos[(d^2*Pi*(a - b*n*Log[x] + b*Log[c*x^n])^2)/2] + I*Sin[(d^2*Pi*(a - b*n*Log[x] + b*Log[c*x^n])^2)/2]))/(2*Sqrt[2]*(c*x^n)^n^(-1))","A",0
57,1,164,65,0.1256384,"\int \frac{S\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x} \, dx","Integrate[FresnelS[d*(a + b*Log[c*x^n])]/x,x]","-\frac{\sin \left(\frac{1}{2} \pi  a^2 d^2\right) \sin \left(\pi  a b d^2 \log \left(c x^n\right)+\frac{1}{2} \pi  b^2 d^2 \log ^2\left(c x^n\right)\right)}{\pi  b d n}+\frac{\cos \left(\frac{1}{2} \pi  a^2 d^2\right) \cos \left(\pi  a b d^2 \log \left(c x^n\right)+\frac{1}{2} \pi  b^2 d^2 \log ^2\left(c x^n\right)\right)}{\pi  b d n}+\frac{a S\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{b n}+\frac{\log \left(c x^n\right) S\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{n}","\frac{\cos \left(\frac{1}{2} \pi  d^2 \left(a+b \log \left(c x^n\right)\right)^2\right)}{\pi  b d n}+\frac{\left(a+b \log \left(c x^n\right)\right) S\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{b n}",1,"(Cos[(a^2*d^2*Pi)/2]*Cos[a*b*d^2*Pi*Log[c*x^n] + (b^2*d^2*Pi*Log[c*x^n]^2)/2])/(b*d*n*Pi) + (a*FresnelS[d*(a + b*Log[c*x^n])])/(b*n) + (FresnelS[d*(a + b*Log[c*x^n])]*Log[c*x^n])/n - (Sin[(a^2*d^2*Pi)/2]*Sin[a*b*d^2*Pi*Log[c*x^n] + (b^2*d^2*Pi*Log[c*x^n]^2)/2])/(b*d*n*Pi)","B",1
58,1,195,217,4.4243839,"\int \frac{S\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^2} \, dx","Integrate[FresnelS[d*(a + b*Log[c*x^n])]/x^2,x]","-\frac{4 S\left(d \left(a+b \log \left(c x^n\right)\right)\right)+\sqrt[4]{-1} \sqrt{2} \left(c x^n\right)^{\frac{1}{n}} e^{\frac{2 a b n-\frac{i}{\pi  d^2}}{2 b^2 n^2}} \left(e^{\frac{i}{\pi  b^2 d^2 n^2}} \text{erfi}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(\pi  a b d^2 n+\pi  b^2 d^2 n \log \left(c x^n\right)+i\right)}{\sqrt{\pi } b d n}\right)+i \text{erfi}\left(\frac{(-1)^{3/4} \left(\pi  a b d^2 n+\pi  b^2 d^2 n \log \left(c x^n\right)-i\right)}{\sqrt{2 \pi } b d n}\right)\right)}{4 x}","\frac{\left(\frac{1}{4}-\frac{i}{4}\right) \left(c x^n\right)^{\frac{1}{n}} e^{\frac{2 a b n+\frac{i}{\pi  d^2}}{2 b^2 n^2}} \text{erf}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(-i \pi  a b d^2-i \pi  b^2 d^2 \log \left(c x^n\right)+\frac{1}{n}\right)}{\sqrt{\pi } b d}\right)}{x}+\frac{\left(\frac{1}{4}-\frac{i}{4}\right) \left(c x^n\right)^{\frac{1}{n}} e^{\frac{2 a b n-\frac{i}{\pi  d^2}}{2 b^2 n^2}} \text{erfi}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(i \pi  a b d^2+i \pi  b^2 d^2 \log \left(c x^n\right)+\frac{1}{n}\right)}{\sqrt{\pi } b d}\right)}{x}-\frac{S\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x}",1,"-1/4*((-1)^(1/4)*Sqrt[2]*E^((2*a*b*n - I/(d^2*Pi))/(2*b^2*n^2))*(c*x^n)^n^(-1)*(I*Erfi[((-1)^(3/4)*(-I + a*b*d^2*n*Pi + b^2*d^2*n*Pi*Log[c*x^n]))/(b*d*n*Sqrt[2*Pi])] + E^(I/(b^2*d^2*n^2*Pi))*Erfi[((1/2 + I/2)*(I + a*b*d^2*n*Pi + b^2*d^2*n*Pi*Log[c*x^n]))/(b*d*n*Sqrt[Pi])]) + 4*FresnelS[d*(a + b*Log[c*x^n])])/x","A",1
59,1,200,228,4.5132555,"\int \frac{S\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^3} \, dx","Integrate[FresnelS[d*(a + b*Log[c*x^n])]/x^3,x]","-\frac{S\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{2 x^2}-\frac{\sqrt[4]{-1} \left(e^{\frac{4 i}{\pi  b^2 d^2 n^2}} \text{erfi}\left(\frac{\sqrt[4]{-1} \left(\pi  a b d^2 n+\pi  b^2 d^2 n \log \left(c x^n\right)+2 i\right)}{\sqrt{2 \pi } b d n}\right)+i \text{erfi}\left(\frac{(-1)^{3/4} \left(\pi  a b d^2 n+\pi  b^2 d^2 n \log \left(c x^n\right)-2 i\right)}{\sqrt{2 \pi } b d n}\right)\right) \exp \left(\frac{2 \left(\frac{a n}{b}-\frac{i}{\pi  b^2 d^2}+n \left(\log \left(c x^n\right)-n \log (x)\right)\right)}{n^2}\right)}{4 \sqrt{2}}","\frac{\left(\frac{1}{8}-\frac{i}{8}\right) \left(c x^n\right)^{2/n} e^{\frac{2 \pi  a b d^2 n+2 i}{\pi  b^2 d^2 n^2}} \text{erf}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(-i \pi  a b d^2-i \pi  b^2 d^2 \log \left(c x^n\right)+\frac{2}{n}\right)}{\sqrt{\pi } b d}\right)}{x^2}+\frac{\left(\frac{1}{8}-\frac{i}{8}\right) \left(c x^n\right)^{2/n} e^{-\frac{2 \left(-\pi  a b d^2 n+i\right)}{\pi  b^2 d^2 n^2}} \text{erfi}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(i \pi  a b d^2+i \pi  b^2 d^2 \log \left(c x^n\right)+\frac{2}{n}\right)}{\sqrt{\pi } b d}\right)}{x^2}-\frac{S\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{2 x^2}",1,"-1/4*((-1)^(1/4)*E^((2*((a*n)/b - I/(b^2*d^2*Pi) + n*(-(n*Log[x]) + Log[c*x^n])))/n^2)*(I*Erfi[((-1)^(3/4)*(-2*I + a*b*d^2*n*Pi + b^2*d^2*n*Pi*Log[c*x^n]))/(b*d*n*Sqrt[2*Pi])] + E^((4*I)/(b^2*d^2*n^2*Pi))*Erfi[((-1)^(1/4)*(2*I + a*b*d^2*n*Pi + b^2*d^2*n*Pi*Log[c*x^n]))/(b*d*n*Sqrt[2*Pi])]))/Sqrt[2] - FresnelS[d*(a + b*Log[c*x^n])]/(2*x^2)","A",1
60,1,244,280,6.2247748,"\int (e x)^m S\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[(e*x)^m*FresnelS[d*(a + b*Log[c*x^n])],x]","\frac{(e x)^m \left(4 x S\left(d \left(a+b \log \left(c x^n\right)\right)\right)-\sqrt[4]{-1} \sqrt{2} x^{-m} \exp \left(-\frac{(m+1) \left(2 \pi  a b d^2 n+2 \pi  b^2 d^2 n \left(\log \left(c x^n\right)-n \log (x)\right)+i m+i\right)}{2 \pi  b^2 d^2 n^2}\right) \left(\text{erf}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(\pi  a b d^2 n+\pi  b^2 d^2 n \log \left(c x^n\right)+i m+i\right)}{\sqrt{\pi } b d n}\right)+e^{\frac{i (m+1)^2}{\pi  b^2 d^2 n^2}} \text{erfi}\left(\frac{(-1)^{3/4} \left(i \pi  a b d^2 n+i \pi  b^2 d^2 n \log \left(c x^n\right)+m+1\right)}{\sqrt{2 \pi } b d n}\right)\right)\right)}{4 (m+1)}","\frac{\left(\frac{1}{4}-\frac{i}{4}\right) x (e x)^m \left(c x^n\right)^{-\frac{m+1}{n}} \exp \left(\frac{i (m+1) \left(2 i \pi  a b d^2 n+m+1\right)}{2 \pi  b^2 d^2 n^2}\right) \text{erf}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(i \pi  a b d^2 n+i \pi  b^2 d^2 n \log \left(c x^n\right)+m+1\right)}{\sqrt{\pi } b d n}\right)}{m+1}+\frac{\left(\frac{1}{4}-\frac{i}{4}\right) x (e x)^m \left(c x^n\right)^{-\frac{m+1}{n}} \exp \left(-\frac{i (m+1) \left(-2 i \pi  a b d^2 n+m+1\right)}{2 \pi  b^2 d^2 n^2}\right) \text{erfi}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(-i \pi  a b d^2 n-i \pi  b^2 d^2 n \log \left(c x^n\right)+m+1\right)}{\sqrt{\pi } b d n}\right)}{m+1}+\frac{(e x)^{m+1} S\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e (m+1)}",1,"((e*x)^m*(-(((-1)^(1/4)*Sqrt[2]*(Erf[((1/2 + I/2)*(I + I*m + a*b*d^2*n*Pi + b^2*d^2*n*Pi*Log[c*x^n]))/(b*d*n*Sqrt[Pi])] + E^((I*(1 + m)^2)/(b^2*d^2*n^2*Pi))*Erfi[((-1)^(3/4)*(1 + m + I*a*b*d^2*n*Pi + I*b^2*d^2*n*Pi*Log[c*x^n]))/(b*d*n*Sqrt[2*Pi])]))/(E^(((1 + m)*(I + I*m + 2*a*b*d^2*n*Pi + 2*b^2*d^2*n*Pi*(-(n*Log[x]) + Log[c*x^n])))/(2*b^2*d^2*n^2*Pi))*x^m)) + 4*x*FresnelS[d*(a + b*Log[c*x^n])]))/(4*(1 + m))","A",1
61,0,0,64,0.0330034,"\int e^{c+\frac{1}{2} i b^2 \pi  x^2} S(b x) \, dx","Integrate[E^(c + (I/2)*b^2*Pi*x^2)*FresnelS[b*x],x]","\int e^{c+\frac{1}{2} i b^2 \pi  x^2} S(b x) \, dx","\frac{1}{4} i b e^c x^2 \, _2F_2\left(1,1;\frac{3}{2},2;\frac{1}{2} i b^2 \pi  x^2\right)-\frac{e^c \text{erfi}\left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\pi } b x\right)^2}{8 b}",1,"Integrate[E^(c + (I/2)*b^2*Pi*x^2)*FresnelS[b*x], x]","F",-1
62,0,0,64,0.0467307,"\int e^{c-\frac{1}{2} i b^2 \pi  x^2} S(b x) \, dx","Integrate[E^(c - (I/2)*b^2*Pi*x^2)*FresnelS[b*x],x]","\int e^{c-\frac{1}{2} i b^2 \pi  x^2} S(b x) \, dx","\frac{e^c \text{erf}\left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\pi } b x\right)^2}{8 b}-\frac{1}{4} i b e^c x^2 \, _2F_2\left(1,1;\frac{3}{2},2;-\frac{1}{2} i b^2 \pi  x^2\right)",1,"Integrate[E^(c - (I/2)*b^2*Pi*x^2)*FresnelS[b*x], x]","F",-1
63,0,0,101,0.0626508,"\int S(b x) \sin \left(c+\frac{1}{2} b^2 \pi  x^2\right) \, dx","Integrate[FresnelS[b*x]*Sin[c + (b^2*Pi*x^2)/2],x]","\int S(b x) \sin \left(c+\frac{1}{2} b^2 \pi  x^2\right) \, dx","-\frac{1}{8} i b x^2 \sin (c) \, _2F_2\left(1,1;\frac{3}{2},2;-\frac{1}{2} i b^2 \pi  x^2\right)+\frac{1}{8} i b x^2 \sin (c) \, _2F_2\left(1,1;\frac{3}{2},2;\frac{1}{2} i b^2 \pi  x^2\right)+\frac{\sin (c) C(b x) S(b x)}{2 b}+\frac{\cos (c) S(b x)^2}{2 b}",1,"Integrate[FresnelS[b*x]*Sin[c + (b^2*Pi*x^2)/2], x]","F",-1
64,0,0,101,0.0544131,"\int \cos \left(c+\frac{1}{2} b^2 \pi  x^2\right) S(b x) \, dx","Integrate[Cos[c + (b^2*Pi*x^2)/2]*FresnelS[b*x],x]","\int \cos \left(c+\frac{1}{2} b^2 \pi  x^2\right) S(b x) \, dx","-\frac{1}{8} i b x^2 \cos (c) \, _2F_2\left(1,1;\frac{3}{2},2;-\frac{1}{2} i b^2 \pi  x^2\right)+\frac{1}{8} i b x^2 \cos (c) \, _2F_2\left(1,1;\frac{3}{2},2;\frac{1}{2} i b^2 \pi  x^2\right)+\frac{\cos (c) C(b x) S(b x)}{2 b}-\frac{\sin (c) S(b x)^2}{2 b}",1,"Integrate[Cos[c + (b^2*Pi*x^2)/2]*FresnelS[b*x], x]","F",-1
65,1,13,13,0.003599,"\int S(b x)^2 \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Integrate[FresnelS[b*x]^2*Sin[(b^2*Pi*x^2)/2],x]","\frac{S(b x)^3}{3 b}","\frac{S(b x)^3}{3 b}",1,"FresnelS[b*x]^3/(3*b)","A",1
66,1,13,13,0.0028118,"\int S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Integrate[FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2],x]","\frac{S(b x)^2}{2 b}","\frac{S(b x)^2}{2 b}",1,"FresnelS[b*x]^2/(2*b)","A",1
67,1,9,9,0.0099126,"\int \frac{\sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{S(b x)} \, dx","Integrate[Sin[(b^2*Pi*x^2)/2]/FresnelS[b*x],x]","\frac{\log (S(b x))}{b}","\frac{\log (S(b x))}{b}",1,"Log[FresnelS[b*x]]/b","A",1
68,1,11,11,0.0030234,"\int \frac{\sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{S(b x)^2} \, dx","Integrate[Sin[(b^2*Pi*x^2)/2]/FresnelS[b*x]^2,x]","-\frac{1}{b S(b x)}","-\frac{1}{b S(b x)}",1,"-(1/(b*FresnelS[b*x]))","A",1
69,1,13,13,0.0030955,"\int \frac{\sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{S(b x)^3} \, dx","Integrate[Sin[(b^2*Pi*x^2)/2]/FresnelS[b*x]^3,x]","-\frac{1}{2 b S(b x)^2}","-\frac{1}{2 b S(b x)^2}",1,"-1/2*1/(b*FresnelS[b*x]^2)","A",1
70,1,17,17,0.0081337,"\int S(b x)^n \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Integrate[FresnelS[b*x]^n*Sin[(b^2*Pi*x^2)/2],x]","\frac{S(b x)^{n+1}}{b (n+1)}","\frac{S(b x)^{n+1}}{b (n+1)}",1,"FresnelS[b*x]^(1 + n)/(b*(1 + n))","A",1
71,1,232,232,0.013933,"\int x^8 S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Integrate[x^8*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2],x]","\frac{105 S(b x)^2}{2 \pi ^4 b^9}+\frac{105 x^2}{4 \pi ^4 b^7}-\frac{7 x^6}{12 \pi ^2 b^3}-\frac{x^7 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{40 \sin \left(\pi  b^2 x^2\right)}{\pi ^5 b^9}-\frac{105 x S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^4 b^8}+\frac{55 x^2 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^4 b^7}+\frac{35 x^3 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}+\frac{5 x^4 \sin \left(\pi  b^2 x^2\right)}{2 \pi ^3 b^5}+\frac{7 x^5 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{x^6 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}","\frac{105 S(b x)^2}{2 \pi ^4 b^9}+\frac{105 x^2}{4 \pi ^4 b^7}-\frac{7 x^6}{12 \pi ^2 b^3}-\frac{x^7 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{40 \sin \left(\pi  b^2 x^2\right)}{\pi ^5 b^9}-\frac{105 x S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^4 b^8}+\frac{55 x^2 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^4 b^7}+\frac{35 x^3 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}+\frac{5 x^4 \sin \left(\pi  b^2 x^2\right)}{2 \pi ^3 b^5}+\frac{7 x^5 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{x^6 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}",1,"(105*x^2)/(4*b^7*Pi^4) - (7*x^6)/(12*b^3*Pi^2) + (55*x^2*Cos[b^2*Pi*x^2])/(4*b^7*Pi^4) - (x^6*Cos[b^2*Pi*x^2])/(4*b^3*Pi^2) + (35*x^3*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(b^6*Pi^3) - (x^7*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(b^2*Pi) + (105*FresnelS[b*x]^2)/(2*b^9*Pi^4) - (105*x*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^8*Pi^4) + (7*x^5*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^4*Pi^2) - (40*Sin[b^2*Pi*x^2])/(b^9*Pi^5) + (5*x^4*Sin[b^2*Pi*x^2])/(2*b^5*Pi^3)","A",1
72,1,153,216,0.2856706,"\int x^7 S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Integrate[x^7*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2],x]","\frac{-160 S(b x) \left(\pi  b^2 x^2 \left(\pi ^2 b^4 x^4-24\right) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)-6 \left(\pi ^2 b^4 x^4-8\right) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)\right)+2 b x \left(2 \left(-24 \pi ^2 b^4 x^4+85 \pi  b^2 x^2 \sin \left(\pi  b^2 x^2\right)+960\right)+\left(735-20 \pi ^2 b^4 x^4\right) \cos \left(\pi  b^2 x^2\right)\right)-2655 \sqrt{2} C\left(\sqrt{2} b x\right)}{160 \pi ^4 b^8}","-\frac{531 C\left(\sqrt{2} b x\right)}{16 \sqrt{2} \pi ^4 b^8}+\frac{24 x}{\pi ^4 b^7}-\frac{3 x^5}{5 \pi ^2 b^3}-\frac{x^6 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{48 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^4 b^8}+\frac{147 x \cos \left(\pi  b^2 x^2\right)}{16 \pi ^4 b^7}+\frac{24 x^2 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}+\frac{17 x^3 \sin \left(\pi  b^2 x^2\right)}{8 \pi ^3 b^5}+\frac{6 x^4 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{x^5 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}",1,"(-2655*Sqrt[2]*FresnelC[Sqrt[2]*b*x] - 160*FresnelS[b*x]*(b^2*Pi*x^2*(-24 + b^4*Pi^2*x^4)*Cos[(b^2*Pi*x^2)/2] - 6*(-8 + b^4*Pi^2*x^4)*Sin[(b^2*Pi*x^2)/2]) + 2*b*x*((735 - 20*b^4*Pi^2*x^4)*Cos[b^2*Pi*x^2] + 2*(960 - 24*b^4*Pi^2*x^4 + 85*b^2*Pi*x^2*Sin[b^2*Pi*x^2])))/(160*b^8*Pi^4)","A",1
73,0,0,248,0.5285351,"\int x^6 S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Integrate[x^6*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2],x]","\int x^6 S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","\frac{15 i x^2 \, _2F_2\left(1,1;\frac{3}{2},2;-\frac{1}{2} i b^2 \pi  x^2\right)}{8 \pi ^3 b^5}-\frac{15 i x^2 \, _2F_2\left(1,1;\frac{3}{2},2;\frac{1}{2} i b^2 \pi  x^2\right)}{8 \pi ^3 b^5}-\frac{15 C(b x) S(b x)}{2 \pi ^3 b^7}-\frac{5 x^4}{8 \pi ^2 b^3}-\frac{x^5 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{11 \cos \left(\pi  b^2 x^2\right)}{2 \pi ^4 b^7}+\frac{15 x S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}+\frac{7 x^2 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^3 b^5}+\frac{5 x^3 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{x^4 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}",1,"Integrate[x^6*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2], x]","F",-1
74,1,120,158,0.1772216,"\int x^5 S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Integrate[x^5*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2],x]","-\frac{32 \pi  b^3 x^3-66 b x \sin \left(\pi  b^2 x^2\right)+48 S(b x) \left(\left(\pi ^2 b^4 x^4-8\right) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)-4 \pi  b^2 x^2 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)\right)+12 \pi  b^3 x^3 \cos \left(\pi  b^2 x^2\right)+129 \sqrt{2} S\left(\sqrt{2} b x\right)}{48 \pi ^3 b^6}","-\frac{43 S\left(\sqrt{2} b x\right)}{8 \sqrt{2} \pi ^3 b^6}-\frac{2 x^3}{3 \pi ^2 b^3}-\frac{x^4 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{8 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}+\frac{11 x \sin \left(\pi  b^2 x^2\right)}{8 \pi ^3 b^5}+\frac{4 x^2 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{x^3 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}",1,"-1/48*(32*b^3*Pi*x^3 + 12*b^3*Pi*x^3*Cos[b^2*Pi*x^2] + 129*Sqrt[2]*FresnelS[Sqrt[2]*b*x] + 48*FresnelS[b*x]*((-8 + b^4*Pi^2*x^4)*Cos[(b^2*Pi*x^2)/2] - 4*b^2*Pi*x^2*Sin[(b^2*Pi*x^2)/2]) - 66*b*x*Sin[b^2*Pi*x^2])/(b^6*Pi^3)","A",1
75,1,120,120,0.0067691,"\int x^4 S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Integrate[x^4*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2],x]","-\frac{3 S(b x)^2}{2 \pi ^2 b^5}-\frac{3 x^2}{4 \pi ^2 b^3}-\frac{x^3 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{\sin \left(\pi  b^2 x^2\right)}{\pi ^3 b^5}+\frac{3 x S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{x^2 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}","-\frac{3 S(b x)^2}{2 \pi ^2 b^5}-\frac{3 x^2}{4 \pi ^2 b^3}-\frac{x^3 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{\sin \left(\pi  b^2 x^2\right)}{\pi ^3 b^5}+\frac{3 x S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{x^2 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}",1,"(-3*x^2)/(4*b^3*Pi^2) - (x^2*Cos[b^2*Pi*x^2])/(4*b^3*Pi^2) - (x^3*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(b^2*Pi) - (3*FresnelS[b*x]^2)/(2*b^5*Pi^2) + (3*x*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^4*Pi^2) + Sin[b^2*Pi*x^2]/(b^5*Pi^3)","A",1
76,1,83,105,0.1123374,"\int x^3 S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Integrate[x^3*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2],x]","\frac{-8 S(b x) \left(\pi  b^2 x^2 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)-2 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)\right)-2 b x \left(\cos \left(\pi  b^2 x^2\right)+4\right)+5 \sqrt{2} C\left(\sqrt{2} b x\right)}{8 \pi ^2 b^4}","\frac{5 C\left(\sqrt{2} b x\right)}{4 \sqrt{2} \pi ^2 b^4}-\frac{x}{\pi ^2 b^3}-\frac{x^2 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{2 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{x \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}",1,"(-2*b*x*(4 + Cos[b^2*Pi*x^2]) + 5*Sqrt[2]*FresnelC[Sqrt[2]*b*x] - 8*FresnelS[b*x]*(b^2*Pi*x^2*Cos[(b^2*Pi*x^2)/2] - 2*Sin[(b^2*Pi*x^2)/2]))/(8*b^4*Pi^2)","A",1
77,0,0,137,0.2409093,"\int x^2 S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Integrate[x^2*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2],x]","\int x^2 S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","-\frac{i x^2 \, _2F_2\left(1,1;\frac{3}{2},2;-\frac{1}{2} i b^2 \pi  x^2\right)}{8 \pi  b}+\frac{i x^2 \, _2F_2\left(1,1;\frac{3}{2},2;\frac{1}{2} i b^2 \pi  x^2\right)}{8 \pi  b}+\frac{C(b x) S(b x)}{2 \pi  b^3}-\frac{x S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{\cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}",1,"Integrate[x^2*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2], x]","F",-1
78,1,44,49,0.0325929,"\int x S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Integrate[x*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2],x]","\frac{\sqrt{2} S\left(\sqrt{2} b x\right)-4 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi  b^2}","\frac{S\left(\sqrt{2} b x\right)}{2 \sqrt{2} \pi  b^2}-\frac{S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}",1,"(-4*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x] + Sqrt[2]*FresnelS[Sqrt[2]*b*x])/(4*b^2*Pi)","A",1
79,1,13,13,0.002056,"\int S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Integrate[FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2],x]","\frac{S(b x)^2}{2 b}","\frac{S(b x)^2}{2 b}",1,"FresnelS[b*x]^2/(2*b)","A",1
80,0,0,23,0.0348677,"\int \frac{S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x} \, dx","Integrate[(FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/x,x]","\int \frac{S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x} \, dx","\text{Int}\left(\frac{S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)",0,"Integrate[(FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/x, x]","A",-1
81,0,0,23,0.0420031,"\int \frac{S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^2} \, dx","Integrate[(FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/x^2,x]","\int \frac{S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^2} \, dx","\text{Int}\left(\frac{S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x^2},x\right)",0,"Integrate[(FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/x^2, x]","A",-1
82,0,0,102,0.0436524,"\int \frac{S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^3} \, dx","Integrate[(FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/x^3,x]","\int \frac{S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^3} \, dx","\frac{1}{2} \pi  b^2 \text{Int}\left(\frac{S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)-\frac{S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{2 x^2}+\frac{\pi  b^2 S\left(\sqrt{2} b x\right)}{2 \sqrt{2}}+\frac{b \cos \left(\pi  b^2 x^2\right)}{4 x}-\frac{b}{4 x}",0,"Integrate[(FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/x^3, x]","A",-1
83,1,109,109,0.0128951,"\int \frac{S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^4} \, dx","Integrate[(FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/x^4,x]","-\frac{1}{6} \pi ^2 b^3 S(b x)^2-\frac{\pi  b^2 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 x}-\frac{S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 x^3}+\frac{b \cos \left(\pi  b^2 x^2\right)}{12 x^2}+\frac{1}{6} \pi  b^3 \text{Si}\left(b^2 \pi  x^2\right)-\frac{b}{12 x^2}","-\frac{1}{6} \pi ^2 b^3 S(b x)^2-\frac{\pi  b^2 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 x}-\frac{S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 x^3}+\frac{b \cos \left(\pi  b^2 x^2\right)}{12 x^2}+\frac{1}{6} \pi  b^3 \text{Si}\left(b^2 \pi  x^2\right)-\frac{b}{12 x^2}",1,"-1/12*b/x^2 + (b*Cos[b^2*Pi*x^2])/(12*x^2) - (b^2*Pi*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(3*x) - (b^3*Pi^2*FresnelS[b*x]^2)/6 - (FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(3*x^3) + (b^3*Pi*SinIntegral[b^2*Pi*x^2])/6","A",1
84,0,0,153,0.0327563,"\int \frac{S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^5} \, dx","Integrate[(FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/x^5,x]","\int \frac{S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^5} \, dx","-\frac{1}{8} \pi ^2 b^4 \text{Int}\left(\frac{S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)+\frac{7 \pi ^2 b^4 C\left(\sqrt{2} b x\right)}{24 \sqrt{2}}-\frac{\pi  b^2 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{8 x^2}-\frac{S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 x^4}+\frac{b \cos \left(\pi  b^2 x^2\right)}{24 x^3}-\frac{7 \pi  b^3 \sin \left(\pi  b^2 x^2\right)}{48 x}-\frac{b}{24 x^3}",0,"Integrate[(FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/x^5, x]","A",-1
85,0,0,148,0.0356222,"\int \frac{S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^6} \, dx","Integrate[(FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/x^6,x]","\int \frac{S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^6} \, dx","-\frac{1}{15} \pi ^2 b^4 \text{Int}\left(\frac{S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x^2},x\right)-\frac{S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 x^5}-\frac{\pi  b^2 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{15 x^3}+\frac{b \cos \left(\pi  b^2 x^2\right)}{40 x^4}+\frac{1}{24} \pi ^2 b^5 \text{Ci}\left(b^2 \pi  x^2\right)-\frac{\pi  b^3 \sin \left(\pi  b^2 x^2\right)}{24 x^2}-\frac{b}{40 x^4}",0,"Integrate[(FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/x^6, x]","A",-1
86,0,0,241,0.03083,"\int \frac{S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^7} \, dx","Integrate[(FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/x^7,x]","\int \frac{S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^7} \, dx","-\frac{1}{48} \pi ^3 b^6 \text{Int}\left(\frac{S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)-\frac{1}{45} \sqrt{2} \pi ^3 b^6 S\left(\sqrt{2} b x\right)-\frac{7 \pi ^3 b^6 S\left(\sqrt{2} b x\right)}{144 \sqrt{2}}+\frac{\pi ^2 b^5}{96 x}-\frac{S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 x^6}-\frac{\pi  b^2 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{24 x^4}+\frac{b \cos \left(\pi  b^2 x^2\right)}{60 x^5}-\frac{67 \pi ^2 b^5 \cos \left(\pi  b^2 x^2\right)}{1440 x}+\frac{\pi ^2 b^4 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{48 x^2}-\frac{13 \pi  b^3 \sin \left(\pi  b^2 x^2\right)}{720 x^3}-\frac{b}{60 x^5}",0,"Integrate[(FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/x^7, x]","A",-1
87,1,224,224,0.0171016,"\int \frac{S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^8} \, dx","Integrate[(FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/x^8,x]","\frac{1}{210} \pi ^4 b^7 S(b x)^2+\frac{\pi ^2 b^5}{420 x^2}-\frac{S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 x^7}-\frac{\pi  b^2 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{35 x^5}+\frac{b \cos \left(\pi  b^2 x^2\right)}{84 x^6}-\frac{1}{70} \pi ^3 b^7 \text{Si}\left(b^2 \pi  x^2\right)+\frac{\pi ^3 b^6 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{105 x}-\frac{\pi ^2 b^5 \cos \left(\pi  b^2 x^2\right)}{84 x^2}+\frac{\pi ^2 b^4 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{105 x^3}-\frac{\pi  b^3 \sin \left(\pi  b^2 x^2\right)}{105 x^4}-\frac{b}{84 x^6}","\frac{1}{210} \pi ^4 b^7 S(b x)^2+\frac{\pi ^2 b^5}{420 x^2}-\frac{S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 x^7}-\frac{\pi  b^2 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{35 x^5}+\frac{b \cos \left(\pi  b^2 x^2\right)}{84 x^6}-\frac{1}{70} \pi ^3 b^7 \text{Si}\left(b^2 \pi  x^2\right)+\frac{\pi ^3 b^6 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{105 x}-\frac{\pi ^2 b^5 \cos \left(\pi  b^2 x^2\right)}{84 x^2}+\frac{\pi ^2 b^4 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{105 x^3}-\frac{\pi  b^3 \sin \left(\pi  b^2 x^2\right)}{105 x^4}-\frac{b}{84 x^6}",1,"-1/84*b/x^6 + (b^5*Pi^2)/(420*x^2) + (b*Cos[b^2*Pi*x^2])/(84*x^6) - (b^5*Pi^2*Cos[b^2*Pi*x^2])/(84*x^2) - (b^2*Pi*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(35*x^5) + (b^6*Pi^3*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(105*x) + (b^7*Pi^4*FresnelS[b*x]^2)/210 - (FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(7*x^7) + (b^4*Pi^2*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(105*x^3) - (b^3*Pi*Sin[b^2*Pi*x^2])/(105*x^4) - (b^7*Pi^3*SinIntegral[b^2*Pi*x^2])/70","A",1
88,0,0,268,0.0359743,"\int \frac{S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^9} \, dx","Integrate[(FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/x^9,x]","\int \frac{S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^9} \, dx","\frac{1}{384} \pi ^4 b^8 \text{Int}\left(\frac{S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)-\frac{853 \pi ^4 b^8 C\left(\sqrt{2} b x\right)}{40320 \sqrt{2}}+\frac{\pi ^2 b^5}{1152 x^3}-\frac{S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{8 x^8}-\frac{\pi  b^2 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{48 x^6}+\frac{b \cos \left(\pi  b^2 x^2\right)}{112 x^7}+\frac{853 \pi ^3 b^7 \sin \left(\pi  b^2 x^2\right)}{80640 x}+\frac{\pi ^3 b^6 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{384 x^2}-\frac{187 \pi ^2 b^5 \cos \left(\pi  b^2 x^2\right)}{40320 x^3}+\frac{\pi ^2 b^4 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{192 x^4}-\frac{19 \pi  b^3 \sin \left(\pi  b^2 x^2\right)}{3360 x^5}-\frac{b}{112 x^7}",0,"Integrate[(FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/x^9, x]","A",-1
89,0,0,263,0.0417811,"\int \frac{S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^{10}} \, dx","Integrate[(FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/x^10,x]","\int \frac{S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^{10}} \, dx","\frac{1}{945} \pi ^4 b^8 \text{Int}\left(\frac{S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x^2},x\right)+\frac{\pi ^2 b^5}{2520 x^4}-\frac{S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{9 x^9}-\frac{\pi  b^2 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{63 x^7}+\frac{b \cos \left(\pi  b^2 x^2\right)}{144 x^8}-\frac{5 \pi ^4 b^9 \text{Ci}\left(b^2 \pi  x^2\right)}{2016}+\frac{5 \pi ^3 b^7 \sin \left(\pi  b^2 x^2\right)}{2016 x^2}+\frac{\pi ^3 b^6 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{945 x^3}-\frac{67 \pi ^2 b^5 \cos \left(\pi  b^2 x^2\right)}{30240 x^4}+\frac{\pi ^2 b^4 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{315 x^5}-\frac{11 \pi  b^3 \sin \left(\pi  b^2 x^2\right)}{3024 x^6}-\frac{b}{144 x^8}",0,"Integrate[(FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/x^10, x]","A",-1
90,0,0,22,0.0880721,"\int \cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x)^n \, dx","Integrate[Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x]^n,x]","\int \cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x)^n \, dx","\text{Int}\left(\cos \left(\frac{1}{2} \pi  b^2 x^2\right) S(b x)^n,x\right)",0,"Integrate[Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x]^n, x]","A",-1
91,0,0,307,0.0577194,"\int x^8 \cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x) \, dx","Integrate[x^8*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x],x]","\int x^8 \cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x) \, dx","-\frac{105 i x^2 \, _2F_2\left(1,1;\frac{3}{2},2;-\frac{1}{2} i b^2 \pi  x^2\right)}{8 \pi ^4 b^7}+\frac{105 i x^2 \, _2F_2\left(1,1;\frac{3}{2},2;\frac{1}{2} i b^2 \pi  x^2\right)}{8 \pi ^4 b^7}+\frac{105 C(b x) S(b x)}{2 \pi ^4 b^9}+\frac{35 x^4}{8 \pi ^3 b^5}+\frac{x^7 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{40 \cos \left(\pi  b^2 x^2\right)}{\pi ^5 b^9}-\frac{105 x S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^4 b^8}-\frac{55 x^2 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^4 b^7}-\frac{35 x^3 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}+\frac{5 x^4 \cos \left(\pi  b^2 x^2\right)}{2 \pi ^3 b^5}+\frac{7 x^5 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}+\frac{x^6 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}-\frac{x^8}{16 \pi  b}",1,"Integrate[x^8*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x], x]","F",-1
92,1,163,217,0.2120964,"\int x^7 \cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x) \, dx","Integrate[x^7*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x],x]","\frac{-16 \pi ^3 b^7 x^7+896 \pi  b^3 x^3-2058 b x \sin \left(\pi  b^2 x^2\right)+56 \pi ^2 b^5 x^5 \sin \left(\pi  b^2 x^2\right)+224 S(b x) \left(\pi  b^2 x^2 \left(\pi ^2 b^4 x^4-24\right) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)+6 \left(\pi ^2 b^4 x^4-8\right) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)\right)+476 \pi  b^3 x^3 \cos \left(\pi  b^2 x^2\right)+3717 \sqrt{2} S\left(\sqrt{2} b x\right)}{224 \pi ^4 b^8}","\frac{531 S\left(\sqrt{2} b x\right)}{16 \sqrt{2} \pi ^4 b^8}+\frac{4 x^3}{\pi ^3 b^5}+\frac{x^6 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{48 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^4 b^8}-\frac{147 x \sin \left(\pi  b^2 x^2\right)}{16 \pi ^4 b^7}-\frac{24 x^2 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}+\frac{17 x^3 \cos \left(\pi  b^2 x^2\right)}{8 \pi ^3 b^5}+\frac{6 x^4 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}+\frac{x^5 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}-\frac{x^7}{14 \pi  b}",1,"(896*b^3*Pi*x^3 - 16*b^7*Pi^3*x^7 + 476*b^3*Pi*x^3*Cos[b^2*Pi*x^2] + 3717*Sqrt[2]*FresnelS[Sqrt[2]*b*x] + 224*FresnelS[b*x]*(6*(-8 + b^4*Pi^2*x^4)*Cos[(b^2*Pi*x^2)/2] + b^2*Pi*x^2*(-24 + b^4*Pi^2*x^4)*Sin[(b^2*Pi*x^2)/2]) - 2058*b*x*Sin[b^2*Pi*x^2] + 56*b^5*Pi^2*x^5*Sin[b^2*Pi*x^2])/(224*b^8*Pi^4)","A",1
93,1,184,184,0.0129704,"\int x^6 \cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x) \, dx","Integrate[x^6*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x],x]","\frac{15 S(b x)^2}{2 \pi ^3 b^7}+\frac{15 x^2}{4 \pi ^3 b^5}+\frac{x^5 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{11 \sin \left(\pi  b^2 x^2\right)}{2 \pi ^4 b^7}-\frac{15 x S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}+\frac{7 x^2 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^3 b^5}+\frac{5 x^3 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}+\frac{x^4 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}-\frac{x^6}{12 \pi  b}","\frac{15 S(b x)^2}{2 \pi ^3 b^7}+\frac{15 x^2}{4 \pi ^3 b^5}+\frac{x^5 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{11 \sin \left(\pi  b^2 x^2\right)}{2 \pi ^4 b^7}-\frac{15 x S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}+\frac{7 x^2 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^3 b^5}+\frac{5 x^3 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}+\frac{x^4 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}-\frac{x^6}{12 \pi  b}",1,"(15*x^2)/(4*b^5*Pi^3) - x^6/(12*b*Pi) + (7*x^2*Cos[b^2*Pi*x^2])/(4*b^5*Pi^3) + (5*x^3*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(b^4*Pi^2) + (15*FresnelS[b*x]^2)/(2*b^7*Pi^3) - (15*x*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^6*Pi^3) + (x^5*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^2*Pi) - (11*Sin[b^2*Pi*x^2])/(2*b^7*Pi^4) + (x^4*Sin[b^2*Pi*x^2])/(4*b^3*Pi^2)","A",1
94,1,126,166,0.197095,"\int x^5 \cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x) \, dx","Integrate[x^5*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x],x]","\frac{80 S(b x) \left(4 \pi  b^2 x^2 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)+\left(\pi ^2 b^4 x^4-8\right) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)\right)+2 b x \left(-4 \pi ^2 b^4 x^4+10 \pi  b^2 x^2 \sin \left(\pi  b^2 x^2\right)+55 \cos \left(\pi  b^2 x^2\right)+160\right)-215 \sqrt{2} C\left(\sqrt{2} b x\right)}{80 \pi ^3 b^6}","-\frac{43 C\left(\sqrt{2} b x\right)}{8 \sqrt{2} \pi ^3 b^6}+\frac{4 x}{\pi ^3 b^5}+\frac{x^4 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{8 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}+\frac{11 x \cos \left(\pi  b^2 x^2\right)}{8 \pi ^3 b^5}+\frac{4 x^2 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}+\frac{x^3 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}-\frac{x^5}{10 \pi  b}",1,"(-215*Sqrt[2]*FresnelC[Sqrt[2]*b*x] + 80*FresnelS[b*x]*(4*b^2*Pi*x^2*Cos[(b^2*Pi*x^2)/2] + (-8 + b^4*Pi^2*x^4)*Sin[(b^2*Pi*x^2)/2]) + 2*b*x*(160 - 4*b^4*Pi^2*x^4 + 55*Cos[b^2*Pi*x^2] + 10*b^2*Pi*x^2*Sin[b^2*Pi*x^2]))/(80*b^6*Pi^3)","A",1
95,0,0,195,0.0458298,"\int x^4 \cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x) \, dx","Integrate[x^4*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x],x]","\int x^4 \cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x) \, dx","\frac{3 i x^2 \, _2F_2\left(1,1;\frac{3}{2},2;-\frac{1}{2} i b^2 \pi  x^2\right)}{8 \pi ^2 b^3}-\frac{3 i x^2 \, _2F_2\left(1,1;\frac{3}{2},2;\frac{1}{2} i b^2 \pi  x^2\right)}{8 \pi ^2 b^3}-\frac{3 C(b x) S(b x)}{2 \pi ^2 b^5}+\frac{x^3 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{\cos \left(\pi  b^2 x^2\right)}{\pi ^3 b^5}+\frac{3 x S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}+\frac{x^2 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}-\frac{x^4}{8 \pi  b}",1,"Integrate[x^4*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x], x]","F",-1
96,1,90,108,0.0877935,"\int x^3 \cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x) \, dx","Integrate[x^3*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x],x]","\frac{-4 \pi  b^3 x^3+24 S(b x) \left(\pi  b^2 x^2 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)+2 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)\right)+6 b x \sin \left(\pi  b^2 x^2\right)-15 \sqrt{2} S\left(\sqrt{2} b x\right)}{24 \pi ^2 b^4}","-\frac{5 S\left(\sqrt{2} b x\right)}{4 \sqrt{2} \pi ^2 b^4}+\frac{x^2 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{2 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}+\frac{x \sin \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}-\frac{x^3}{6 \pi  b}",1,"(-4*b^3*Pi*x^3 - 15*Sqrt[2]*FresnelS[Sqrt[2]*b*x] + 24*FresnelS[b*x]*(2*Cos[(b^2*Pi*x^2)/2] + b^2*Pi*x^2*Sin[(b^2*Pi*x^2)/2]) + 6*b*x*Sin[b^2*Pi*x^2])/(24*b^4*Pi^2)","A",1
97,1,73,73,0.0065635,"\int x^2 \cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x) \, dx","Integrate[x^2*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x],x]","-\frac{S(b x)^2}{2 \pi  b^3}+\frac{x S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{\sin \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}-\frac{x^2}{4 \pi  b}","-\frac{S(b x)^2}{2 \pi  b^3}+\frac{x S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{\sin \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}-\frac{x^2}{4 \pi  b}",1,"-1/4*x^2/(b*Pi) - FresnelS[b*x]^2/(2*b^3*Pi) + (x*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^2*Pi) + Sin[b^2*Pi*x^2]/(4*b^3*Pi^2)","A",1
98,1,48,59,0.0392019,"\int x \cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x) \, dx","Integrate[x*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x],x]","\frac{4 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)+\sqrt{2} C\left(\sqrt{2} b x\right)-2 b x}{4 \pi  b^2}","\frac{C\left(\sqrt{2} b x\right)}{2 \sqrt{2} \pi  b^2}+\frac{S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{x}{2 \pi  b}",1,"(-2*b*x + Sqrt[2]*FresnelC[Sqrt[2]*b*x] + 4*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(4*b^2*Pi)","A",1
99,0,0,80,0.0164433,"\int \cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x) \, dx","Integrate[Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x],x]","\int \cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x) \, dx","-\frac{1}{8} i b x^2 \, _2F_2\left(1,1;\frac{3}{2},2;-\frac{1}{2} i b^2 \pi  x^2\right)+\frac{1}{8} i b x^2 \, _2F_2\left(1,1;\frac{3}{2},2;\frac{1}{2} i b^2 \pi  x^2\right)+\frac{C(b x) S(b x)}{2 b}",1,"Integrate[Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x], x]","F",-1
100,0,0,23,0.0375308,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x)}{x} \, dx","Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/x,x]","\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x)}{x} \, dx","\text{Int}\left(\frac{S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)",0,"Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/x, x]","A",-1
101,1,48,48,0.0084335,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x)}{x^2} \, dx","Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/x^2,x]","-\frac{S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x}+\frac{1}{4} b \text{Si}\left(b^2 \pi  x^2\right)-\frac{1}{2} \pi  b S(b x)^2","-\frac{S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x}+\frac{1}{4} b \text{Si}\left(b^2 \pi  x^2\right)-\frac{1}{2} \pi  b S(b x)^2",1,"-((Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/x) - (b*Pi*FresnelS[b*x]^2)/2 + (b*SinIntegral[b^2*Pi*x^2])/4","A",1
102,0,0,94,0.0439468,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x)}{x^3} \, dx","Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/x^3,x]","\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x)}{x^3} \, dx","-\frac{1}{2} \pi  b^2 \text{Int}\left(\frac{S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)+\frac{\pi  b^2 C\left(\sqrt{2} b x\right)}{2 \sqrt{2}}-\frac{S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{2 x^2}-\frac{b \sin \left(\pi  b^2 x^2\right)}{4 x}",0,"Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/x^3, x]","A",-1
103,0,0,89,0.0460589,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x)}{x^4} \, dx","Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/x^4,x]","\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x)}{x^4} \, dx","-\frac{1}{3} \pi  b^2 \text{Int}\left(\frac{S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x^2},x\right)-\frac{S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 x^3}-\frac{b \sin \left(\pi  b^2 x^2\right)}{12 x^2}+\frac{1}{12} \pi  b^3 \text{Ci}\left(b^2 \pi  x^2\right)",0,"Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/x^4, x]","A",-1
104,0,0,156,0.0382335,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x)}{x^5} \, dx","Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/x^5,x]","\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x)}{x^5} \, dx","-\frac{1}{8} \pi ^2 b^4 \text{Int}\left(\frac{S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)-\frac{7 \pi ^2 b^4 S\left(\sqrt{2} b x\right)}{24 \sqrt{2}}+\frac{\pi  b^3}{16 x}+\frac{\pi  b^2 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{8 x^2}-\frac{S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 x^4}-\frac{b \sin \left(\pi  b^2 x^2\right)}{24 x^3}-\frac{7 \pi  b^3 \cos \left(\pi  b^2 x^2\right)}{48 x}",0,"Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/x^5, x]","A",-1
105,1,163,163,0.0093911,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x)}{x^6} \, dx","Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/x^6,x]","\frac{1}{30} \pi ^3 b^5 S(b x)^2+\frac{\pi  b^3}{60 x^2}-\frac{S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 x^5}+\frac{\pi  b^2 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{15 x^3}-\frac{b \sin \left(\pi  b^2 x^2\right)}{40 x^4}-\frac{7}{120} \pi ^2 b^5 \text{Si}\left(b^2 \pi  x^2\right)+\frac{\pi ^2 b^4 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{15 x}-\frac{\pi  b^3 \cos \left(\pi  b^2 x^2\right)}{24 x^2}","\frac{1}{30} \pi ^3 b^5 S(b x)^2+\frac{\pi  b^3}{60 x^2}-\frac{S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 x^5}+\frac{\pi  b^2 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{15 x^3}-\frac{b \sin \left(\pi  b^2 x^2\right)}{40 x^4}-\frac{7}{120} \pi ^2 b^5 \text{Si}\left(b^2 \pi  x^2\right)+\frac{\pi ^2 b^4 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{15 x}-\frac{\pi  b^3 \cos \left(\pi  b^2 x^2\right)}{24 x^2}",1,"(b^3*Pi)/(60*x^2) - (b^3*Pi*Cos[b^2*Pi*x^2])/(24*x^2) - (Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(5*x^5) + (b^4*Pi^2*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(15*x) + (b^5*Pi^3*FresnelS[b*x]^2)/30 + (b^2*Pi*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(15*x^3) - (b*Sin[b^2*Pi*x^2])/(40*x^4) - (7*b^5*Pi^2*SinIntegral[b^2*Pi*x^2])/120","A",1
106,0,0,231,0.0387433,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x)}{x^7} \, dx","Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/x^7,x]","\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x)}{x^7} \, dx","\frac{1}{48} \pi ^3 b^6 \text{Int}\left(\frac{S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)-\frac{1}{45} \sqrt{2} \pi ^3 b^6 C\left(\sqrt{2} b x\right)-\frac{7 \pi ^3 b^6 C\left(\sqrt{2} b x\right)}{144 \sqrt{2}}+\frac{\pi  b^3}{144 x^3}-\frac{S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 x^6}+\frac{\pi  b^2 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{24 x^4}-\frac{b \sin \left(\pi  b^2 x^2\right)}{60 x^5}+\frac{67 \pi ^2 b^5 \sin \left(\pi  b^2 x^2\right)}{1440 x}+\frac{\pi ^2 b^4 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{48 x^2}-\frac{13 \pi  b^3 \cos \left(\pi  b^2 x^2\right)}{720 x^3}",0,"Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/x^7, x]","A",-1
107,0,0,202,0.0360845,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x)}{x^8} \, dx","Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/x^8,x]","\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x)}{x^8} \, dx","\frac{1}{105} \pi ^3 b^6 \text{Int}\left(\frac{S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x^2},x\right)+\frac{\pi  b^3}{280 x^4}-\frac{S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 x^7}+\frac{\pi  b^2 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{35 x^5}-\frac{b \sin \left(\pi  b^2 x^2\right)}{84 x^6}-\frac{1}{84} \pi ^3 b^7 \text{Ci}\left(b^2 \pi  x^2\right)+\frac{\pi ^2 b^5 \sin \left(\pi  b^2 x^2\right)}{84 x^2}+\frac{\pi ^2 b^4 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{105 x^3}-\frac{\pi  b^3 \cos \left(\pi  b^2 x^2\right)}{105 x^4}",0,"Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/x^8, x]","A",-1
108,0,0,271,0.0357633,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x)}{x^9} \, dx","Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/x^9,x]","\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x)}{x^9} \, dx","\frac{1}{384} \pi ^4 b^8 \text{Int}\left(\frac{S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)+\frac{853 \pi ^4 b^8 S\left(\sqrt{2} b x\right)}{40320 \sqrt{2}}-\frac{\pi ^3 b^7}{768 x}+\frac{\pi  b^3}{480 x^5}-\frac{S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{8 x^8}+\frac{\pi  b^2 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{48 x^6}-\frac{b \sin \left(\pi  b^2 x^2\right)}{112 x^7}+\frac{853 \pi ^3 b^7 \cos \left(\pi  b^2 x^2\right)}{80640 x}-\frac{\pi ^3 b^6 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{384 x^2}+\frac{187 \pi ^2 b^5 \sin \left(\pi  b^2 x^2\right)}{40320 x^3}+\frac{\pi ^2 b^4 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{192 x^4}-\frac{19 \pi  b^3 \cos \left(\pi  b^2 x^2\right)}{3360 x^5}",0,"Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/x^9, x]","A",-1
109,1,278,278,0.0215079,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x)}{x^{10}} \, dx","Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/x^10,x]","-\frac{\pi ^5 b^9 S(b x)^2}{1890}-\frac{\pi ^3 b^7}{3780 x^2}+\frac{\pi  b^3}{756 x^6}-\frac{S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{9 x^9}+\frac{\pi  b^2 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{63 x^7}-\frac{b \sin \left(\pi  b^2 x^2\right)}{144 x^8}+\frac{83 \pi ^4 b^9 \text{Si}\left(b^2 \pi  x^2\right)}{30240}-\frac{\pi ^4 b^8 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{945 x}+\frac{5 \pi ^3 b^7 \cos \left(\pi  b^2 x^2\right)}{2016 x^2}-\frac{\pi ^3 b^6 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{945 x^3}+\frac{67 \pi ^2 b^5 \sin \left(\pi  b^2 x^2\right)}{30240 x^4}+\frac{\pi ^2 b^4 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{315 x^5}-\frac{11 \pi  b^3 \cos \left(\pi  b^2 x^2\right)}{3024 x^6}","-\frac{\pi ^5 b^9 S(b x)^2}{1890}-\frac{\pi ^3 b^7}{3780 x^2}+\frac{\pi  b^3}{756 x^6}-\frac{S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{9 x^9}+\frac{\pi  b^2 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{63 x^7}-\frac{b \sin \left(\pi  b^2 x^2\right)}{144 x^8}+\frac{83 \pi ^4 b^9 \text{Si}\left(b^2 \pi  x^2\right)}{30240}-\frac{\pi ^4 b^8 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{945 x}+\frac{5 \pi ^3 b^7 \cos \left(\pi  b^2 x^2\right)}{2016 x^2}-\frac{\pi ^3 b^6 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{945 x^3}+\frac{67 \pi ^2 b^5 \sin \left(\pi  b^2 x^2\right)}{30240 x^4}+\frac{\pi ^2 b^4 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{315 x^5}-\frac{11 \pi  b^3 \cos \left(\pi  b^2 x^2\right)}{3024 x^6}",1,"(b^3*Pi)/(756*x^6) - (b^7*Pi^3)/(3780*x^2) - (11*b^3*Pi*Cos[b^2*Pi*x^2])/(3024*x^6) + (5*b^7*Pi^3*Cos[b^2*Pi*x^2])/(2016*x^2) - (Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(9*x^9) + (b^4*Pi^2*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(315*x^5) - (b^8*Pi^4*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(945*x) - (b^9*Pi^5*FresnelS[b*x]^2)/1890 + (b^2*Pi*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(63*x^7) - (b^6*Pi^3*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(945*x^3) - (b*Sin[b^2*Pi*x^2])/(144*x^8) + (67*b^5*Pi^2*Sin[b^2*Pi*x^2])/(30240*x^4) + (83*b^9*Pi^4*SinIntegral[b^2*Pi*x^2])/30240","A",1
110,1,89,124,0.078418,"\int x^7 C(b x) \, dx","Integrate[x^7*FresnelC[b*x],x]","\frac{\left(\pi ^4 b^8 x^8-105\right) C(b x)-7 b x \left(\pi ^2 b^4 x^4-15\right) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)+\pi  b^3 x^3 \left(35-\pi ^2 b^4 x^4\right) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{8 \pi ^4 b^8}","-\frac{105 C(b x)}{8 \pi ^4 b^8}-\frac{x^7 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{8 \pi  b}+\frac{105 x \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{8 \pi ^4 b^7}+\frac{35 x^3 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{8 \pi ^3 b^5}-\frac{7 x^5 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{8 \pi ^2 b^3}+\frac{1}{8} x^8 C(b x)",1,"(-7*b*x*(-15 + b^4*Pi^2*x^4)*Cos[(b^2*Pi*x^2)/2] + (-105 + b^8*Pi^4*x^8)*FresnelC[b*x] + b^3*Pi*x^3*(35 - b^4*Pi^2*x^4)*Sin[(b^2*Pi*x^2)/2])/(8*b^8*Pi^4)","A",1
111,1,83,109,0.0816063,"\int x^6 C(b x) \, dx","Integrate[x^6*FresnelC[b*x],x]","-\frac{6 \left(\pi ^2 b^4 x^4-8\right) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi ^4 b^7}-\frac{x^2 \left(\pi ^2 b^4 x^4-24\right) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi ^3 b^5}+\frac{1}{7} x^7 C(b x)","-\frac{x^6 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi  b}+\frac{48 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi ^4 b^7}+\frac{24 x^2 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi ^3 b^5}-\frac{6 x^4 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi ^2 b^3}+\frac{1}{7} x^7 C(b x)",1,"(-6*(-8 + b^4*Pi^2*x^4)*Cos[(b^2*Pi*x^2)/2])/(7*b^7*Pi^4) + (x^7*FresnelC[b*x])/7 - (x^2*(-24 + b^4*Pi^2*x^4)*Sin[(b^2*Pi*x^2)/2])/(7*b^5*Pi^3)","A",1
112,1,80,99,0.0634966,"\int x^5 C(b x) \, dx","Integrate[x^5*FresnelC[b*x],x]","\frac{\pi ^3 b^6 x^6 C(b x)+b x \left(15-\pi ^2 b^4 x^4\right) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)-5 \pi  b^3 x^3 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)-15 S(b x)}{6 \pi ^3 b^6}","-\frac{5 S(b x)}{2 \pi ^3 b^6}-\frac{x^5 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 \pi  b}+\frac{5 x \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{2 \pi ^3 b^5}-\frac{5 x^3 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 \pi ^2 b^3}+\frac{1}{6} x^6 C(b x)",1,"(-5*b^3*Pi*x^3*Cos[(b^2*Pi*x^2)/2] + b^6*Pi^3*x^6*FresnelC[b*x] - 15*FresnelS[b*x] + b*x*(15 - b^4*Pi^2*x^4)*Sin[(b^2*Pi*x^2)/2])/(6*b^6*Pi^3)","A",1
113,1,71,84,0.0577848,"\int x^4 C(b x) \, dx","Integrate[x^4*FresnelC[b*x],x]","-\frac{4 x^2 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 \pi ^2 b^3}-\frac{\left(\pi ^2 b^4 x^4-8\right) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 \pi ^3 b^5}+\frac{1}{5} x^5 C(b x)","-\frac{x^4 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 \pi  b}+\frac{8 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 \pi ^3 b^5}-\frac{4 x^2 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 \pi ^2 b^3}+\frac{1}{5} x^5 C(b x)",1,"(-4*x^2*Cos[(b^2*Pi*x^2)/2])/(5*b^3*Pi^2) + (x^5*FresnelC[b*x])/5 - ((-8 + b^4*Pi^2*x^4)*Sin[(b^2*Pi*x^2)/2])/(5*b^5*Pi^3)","A",1
114,1,74,74,0.0219281,"\int x^3 C(b x) \, dx","Integrate[x^3*FresnelC[b*x],x]","\frac{3 C(b x)}{4 \pi ^2 b^4}-\frac{x^3 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi  b}-\frac{3 x \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi ^2 b^3}+\frac{1}{4} x^4 C(b x)","\frac{3 C(b x)}{4 \pi ^2 b^4}-\frac{x^3 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi  b}-\frac{3 x \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi ^2 b^3}+\frac{1}{4} x^4 C(b x)",1,"(-3*x*Cos[(b^2*Pi*x^2)/2])/(4*b^3*Pi^2) + (3*FresnelC[b*x])/(4*b^4*Pi^2) + (x^4*FresnelC[b*x])/4 - (x^3*Sin[(b^2*Pi*x^2)/2])/(4*b*Pi)","A",1
115,1,59,59,0.0153429,"\int x^2 C(b x) \, dx","Integrate[x^2*FresnelC[b*x],x]","-\frac{x^2 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 \pi  b}-\frac{2 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 \pi ^2 b^3}+\frac{1}{3} x^3 C(b x)","-\frac{x^2 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 \pi  b}-\frac{2 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 \pi ^2 b^3}+\frac{1}{3} x^3 C(b x)",1,"(-2*Cos[(b^2*Pi*x^2)/2])/(3*b^3*Pi^2) + (x^3*FresnelC[b*x])/3 - (x^2*Sin[(b^2*Pi*x^2)/2])/(3*b*Pi)","A",1
116,1,49,49,0.0133307,"\int x C(b x) \, dx","Integrate[x*FresnelC[b*x],x]","\frac{S(b x)}{2 \pi  b^2}-\frac{x \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{2 \pi  b}+\frac{1}{2} x^2 C(b x)","\frac{S(b x)}{2 \pi  b^2}-\frac{x \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{2 \pi  b}+\frac{1}{2} x^2 C(b x)",1,"(x^2*FresnelC[b*x])/2 + FresnelS[b*x]/(2*b^2*Pi) - (x*Sin[(b^2*Pi*x^2)/2])/(2*b*Pi)","A",1
117,1,27,27,0.0029059,"\int C(b x) \, dx","Integrate[FresnelC[b*x],x]","x C(b x)-\frac{\sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b}","x C(b x)-\frac{\sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b}",1,"x*FresnelC[b*x] - Sin[(b^2*Pi*x^2)/2]/(b*Pi)","A",1
118,0,0,69,0.0184477,"\int \frac{C(b x)}{x} \, dx","Integrate[FresnelC[b*x]/x,x]","\int \frac{C(b x)}{x} \, dx","\frac{1}{2} b x \, _2F_2\left(\frac{1}{2},\frac{1}{2};\frac{3}{2},\frac{3}{2};-\frac{1}{2} i b^2 \pi  x^2\right)+\frac{1}{2} b x \, _2F_2\left(\frac{1}{2},\frac{1}{2};\frac{3}{2},\frac{3}{2};\frac{1}{2} i b^2 \pi  x^2\right)",1,"Integrate[FresnelC[b*x]/x, x]","F",-1
119,1,27,27,0.0156718,"\int \frac{C(b x)}{x^2} \, dx","Integrate[FresnelC[b*x]/x^2,x]","\frac{1}{2} b \text{Ci}\left(\frac{1}{2} b^2 \pi  x^2\right)-\frac{C(b x)}{x}","\frac{1}{2} b \text{Ci}\left(\frac{1}{2} b^2 \pi  x^2\right)-\frac{C(b x)}{x}",1,"(b*CosIntegral[(b^2*Pi*x^2)/2])/2 - FresnelC[b*x]/x","A",1
120,1,44,44,0.0236459,"\int \frac{C(b x)}{x^3} \, dx","Integrate[FresnelC[b*x]/x^3,x]","-\frac{1}{2} \pi  b^2 S(b x)-\frac{b \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{2 x}-\frac{C(b x)}{2 x^2}","-\frac{1}{2} \pi  b^2 S(b x)-\frac{b \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{2 x}-\frac{C(b x)}{2 x^2}",1,"-1/2*(b*Cos[(b^2*Pi*x^2)/2])/x - FresnelC[b*x]/(2*x^2) - (b^2*Pi*FresnelS[b*x])/2","A",1
121,1,52,52,0.0188213,"\int \frac{C(b x)}{x^4} \, dx","Integrate[FresnelC[b*x]/x^4,x]","-\frac{b \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 x^2}-\frac{1}{12} \pi  b^3 \text{Si}\left(\frac{1}{2} b^2 \pi  x^2\right)-\frac{C(b x)}{3 x^3}","-\frac{b \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 x^2}-\frac{1}{12} \pi  b^3 \text{Si}\left(\frac{1}{2} b^2 \pi  x^2\right)-\frac{C(b x)}{3 x^3}",1,"-1/6*(b*Cos[(b^2*Pi*x^2)/2])/x^2 - FresnelC[b*x]/(3*x^3) - (b^3*Pi*SinIntegral[(b^2*Pi*x^2)/2])/12","A",1
122,1,69,69,0.0212496,"\int \frac{C(b x)}{x^5} \, dx","Integrate[FresnelC[b*x]/x^5,x]","-\frac{1}{12} \pi ^2 b^4 C(b x)-\frac{b \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{12 x^3}+\frac{\pi  b^3 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{12 x}-\frac{C(b x)}{4 x^4}","-\frac{1}{12} \pi ^2 b^4 C(b x)-\frac{b \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{12 x^3}+\frac{\pi  b^3 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{12 x}-\frac{C(b x)}{4 x^4}",1,"-1/12*(b*Cos[(b^2*Pi*x^2)/2])/x^3 - (b^4*Pi^2*FresnelC[b*x])/12 - FresnelC[b*x]/(4*x^4) + (b^3*Pi*Sin[(b^2*Pi*x^2)/2])/(12*x)","A",1
123,1,77,77,0.0191939,"\int \frac{C(b x)}{x^6} \, dx","Integrate[FresnelC[b*x]/x^6,x]","-\frac{b \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{20 x^4}-\frac{1}{80} \pi ^2 b^5 \text{Ci}\left(\frac{1}{2} b^2 \pi  x^2\right)+\frac{\pi  b^3 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{40 x^2}-\frac{C(b x)}{5 x^5}","-\frac{b \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{20 x^4}-\frac{1}{80} \pi ^2 b^5 \text{Ci}\left(\frac{1}{2} b^2 \pi  x^2\right)+\frac{\pi  b^3 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{40 x^2}-\frac{C(b x)}{5 x^5}",1,"-1/20*(b*Cos[(b^2*Pi*x^2)/2])/x^4 - (b^5*Pi^2*CosIntegral[(b^2*Pi*x^2)/2])/80 - FresnelC[b*x]/(5*x^5) + (b^3*Pi*Sin[(b^2*Pi*x^2)/2])/(40*x^2)","A",1
124,1,74,94,0.1234041,"\int \frac{C(b x)}{x^7} \, dx","Integrate[FresnelC[b*x]/x^7,x]","\frac{1}{90} \left(\pi ^3 b^6 S(b x)+\frac{b \left(\pi ^2 b^4 x^4-3\right) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x^5}+\frac{\pi  b^3 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x^3}-\frac{15 C(b x)}{x^6}\right)","\frac{1}{90} \pi ^3 b^6 S(b x)-\frac{b \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{30 x^5}+\frac{\pi ^2 b^5 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{90 x}+\frac{\pi  b^3 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{90 x^3}-\frac{C(b x)}{6 x^6}",1,"((b*(-3 + b^4*Pi^2*x^4)*Cos[(b^2*Pi*x^2)/2])/x^5 - (15*FresnelC[b*x])/x^6 + b^6*Pi^3*FresnelS[b*x] + (b^3*Pi*Sin[(b^2*Pi*x^2)/2])/x^3)/90","A",1
125,1,84,102,0.147016,"\int \frac{C(b x)}{x^8} \, dx","Integrate[FresnelC[b*x]/x^8,x]","\frac{1}{672} \left(\pi ^3 b^7 \text{Si}\left(\frac{1}{2} b^2 \pi  x^2\right)+\frac{2 b \left(\pi ^2 b^4 x^4-8\right) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x^6}+\frac{4 \pi  b^3 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x^4}-\frac{96 C(b x)}{x^7}\right)","-\frac{b \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{42 x^6}+\frac{1}{672} \pi ^3 b^7 \text{Si}\left(\frac{1}{2} b^2 \pi  x^2\right)+\frac{\pi ^2 b^5 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{336 x^2}+\frac{\pi  b^3 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{168 x^4}-\frac{C(b x)}{7 x^7}",1,"((2*b*(-8 + b^4*Pi^2*x^4)*Cos[(b^2*Pi*x^2)/2])/x^6 - (96*FresnelC[b*x])/x^7 + (4*b^3*Pi*Sin[(b^2*Pi*x^2)/2])/x^4 + b^7*Pi^3*SinIntegral[(b^2*Pi*x^2)/2])/672","A",1
126,1,85,119,0.0716134,"\int \frac{C(b x)}{x^9} \, dx","Integrate[FresnelC[b*x]/x^9,x]","\frac{\left(\pi ^4 b^8 x^8-105\right) C(b x)+b x \left(\pi ^2 b^4 x^4-15\right) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)+\pi  b^3 x^3 \left(3-\pi ^2 b^4 x^4\right) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{840 x^8}","\frac{1}{840} \pi ^4 b^8 C(b x)-\frac{b \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{56 x^7}-\frac{\pi ^3 b^7 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{840 x}+\frac{\pi ^2 b^5 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{840 x^3}+\frac{\pi  b^3 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{280 x^5}-\frac{C(b x)}{8 x^8}",1,"(b*x*(-15 + b^4*Pi^2*x^4)*Cos[(b^2*Pi*x^2)/2] + (-105 + b^8*Pi^4*x^8)*FresnelC[b*x] + b^3*Pi*x^3*(3 - b^4*Pi^2*x^4)*Sin[(b^2*Pi*x^2)/2])/(840*x^8)","A",1
127,1,96,127,0.1082555,"\int \frac{C(b x)}{x^{10}} \, dx","Integrate[FresnelC[b*x]/x^10,x]","\frac{\pi ^4 b^9 \text{Ci}\left(\frac{1}{2} b^2 \pi  x^2\right)+\frac{4 b \left(\pi ^2 b^4 x^4-24\right) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x^8}-\frac{2 \pi  b^3 \left(\pi ^2 b^4 x^4-8\right) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x^6}-\frac{768 C(b x)}{x^9}}{6912}","-\frac{b \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{72 x^8}+\frac{\pi ^4 b^9 \text{Ci}\left(\frac{1}{2} b^2 \pi  x^2\right)}{6912}-\frac{\pi ^3 b^7 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{3456 x^2}+\frac{\pi ^2 b^5 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{1728 x^4}+\frac{\pi  b^3 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{432 x^6}-\frac{C(b x)}{9 x^9}",1,"((4*b*(-24 + b^4*Pi^2*x^4)*Cos[(b^2*Pi*x^2)/2])/x^8 + b^9*Pi^4*CosIntegral[(b^2*Pi*x^2)/2] - (768*FresnelC[b*x])/x^9 - (2*b^3*Pi*(-8 + b^4*Pi^2*x^4)*Sin[(b^2*Pi*x^2)/2])/x^6)/6912","A",1
128,1,424,298,0.9525208,"\int (c+d x)^3 C(a+b x) \, dx","Integrate[(c + d*x)^3*FresnelC[a + b*x],x]","\frac{\pi  a^3 d^3 \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)-4 \pi  a^2 b c d^2 \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)-\pi  a^2 b d^3 x \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)+C(a+b x) \left(d^3 \left(-\pi ^2 a^4+\pi ^2 b^4 x^4+3\right)+4 \pi ^2 b c d^2 \left(a^3+b^3 x^3\right)+6 \pi ^2 b^2 c^2 d \left(b^2 x^2-a^2\right)+4 \pi ^2 b^3 c^3 (a+b x)\right)-4 \pi  b^3 c^3 \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)-6 \pi  b^3 c^2 d x \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)-4 \pi  b^3 c d^2 x^2 \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)+\pi  b^3 \left(-d^3\right) x^3 \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)+6 \pi  a b^2 c^2 d \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)+4 \pi  a b^2 c d^2 x \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)+\pi  a b^2 d^3 x^2 \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)-8 b c d^2 \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)+6 \pi  d (b c-a d)^2 S(a+b x)-3 b d^3 x \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)+5 a d^3 \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{4 \pi ^2 b^4}","-\frac{d^2 (a+b x)^2 (b c-a d) \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b^4}-\frac{2 d^2 (b c-a d) \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi ^2 b^4}-\frac{(b c-a d)^4 C(a+b x)}{4 b^4 d}+\frac{3 d (b c-a d)^2 S(a+b x)}{2 \pi  b^4}-\frac{(b c-a d)^3 \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b^4}-\frac{3 d (a+b x) (b c-a d)^2 \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{2 \pi  b^4}+\frac{3 d^3 C(a+b x)}{4 \pi ^2 b^4}-\frac{d^3 (a+b x)^3 \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{4 \pi  b^4}-\frac{3 d^3 (a+b x) \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{4 \pi ^2 b^4}+\frac{(c+d x)^4 C(a+b x)}{4 d}",1,"(-8*b*c*d^2*Cos[(Pi*(a + b*x)^2)/2] + 5*a*d^3*Cos[(Pi*(a + b*x)^2)/2] - 3*b*d^3*x*Cos[(Pi*(a + b*x)^2)/2] + (4*b^3*c^3*Pi^2*(a + b*x) + 6*b^2*c^2*d*Pi^2*(-a^2 + b^2*x^2) + 4*b*c*d^2*Pi^2*(a^3 + b^3*x^3) + d^3*(3 - a^4*Pi^2 + b^4*Pi^2*x^4))*FresnelC[a + b*x] + 6*d*(b*c - a*d)^2*Pi*FresnelS[a + b*x] - 4*b^3*c^3*Pi*Sin[(Pi*(a + b*x)^2)/2] + 6*a*b^2*c^2*d*Pi*Sin[(Pi*(a + b*x)^2)/2] - 4*a^2*b*c*d^2*Pi*Sin[(Pi*(a + b*x)^2)/2] + a^3*d^3*Pi*Sin[(Pi*(a + b*x)^2)/2] - 6*b^3*c^2*d*Pi*x*Sin[(Pi*(a + b*x)^2)/2] + 4*a*b^2*c*d^2*Pi*x*Sin[(Pi*(a + b*x)^2)/2] - a^2*b*d^3*Pi*x*Sin[(Pi*(a + b*x)^2)/2] - 4*b^3*c*d^2*Pi*x^2*Sin[(Pi*(a + b*x)^2)/2] + a*b^2*d^3*Pi*x^2*Sin[(Pi*(a + b*x)^2)/2] - b^3*d^3*Pi*x^3*Sin[(Pi*(a + b*x)^2)/2])/(4*b^4*Pi^2)","A",1
129,1,237,194,0.5410269,"\int (c+d x)^2 C(a+b x) \, dx","Integrate[(c + d*x)^2*FresnelC[a + b*x],x]","\frac{-\pi  a^2 d^2 \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)+\pi ^2 C(a+b x) \left(a^3 d^2-3 a^2 b c d+3 a b^2 c^2+b^3 x \left(3 c^2+3 c d x+d^2 x^2\right)\right)-3 \pi  b^2 c^2 \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)-3 \pi  b^2 c d x \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)+\pi  b^2 \left(-d^2\right) x^2 \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)+3 \pi  d (b c-a d) S(a+b x)+3 \pi  a b c d \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)+\pi  a b d^2 x \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)-2 d^2 \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{3 \pi ^2 b^3}","-\frac{(b c-a d)^3 C(a+b x)}{3 b^3 d}+\frac{d (b c-a d) S(a+b x)}{\pi  b^3}-\frac{(b c-a d)^2 \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b^3}-\frac{d (a+b x) (b c-a d) \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b^3}-\frac{d^2 (a+b x)^2 \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{3 \pi  b^3}-\frac{2 d^2 \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{3 \pi ^2 b^3}+\frac{(c+d x)^3 C(a+b x)}{3 d}",1,"(-2*d^2*Cos[(Pi*(a + b*x)^2)/2] + Pi^2*(3*a*b^2*c^2 - 3*a^2*b*c*d + a^3*d^2 + b^3*x*(3*c^2 + 3*c*d*x + d^2*x^2))*FresnelC[a + b*x] + 3*d*(b*c - a*d)*Pi*FresnelS[a + b*x] - 3*b^2*c^2*Pi*Sin[(Pi*(a + b*x)^2)/2] + 3*a*b*c*d*Pi*Sin[(Pi*(a + b*x)^2)/2] - a^2*d^2*Pi*Sin[(Pi*(a + b*x)^2)/2] - 3*b^2*c*d*Pi*x*Sin[(Pi*(a + b*x)^2)/2] + a*b*d^2*Pi*x*Sin[(Pi*(a + b*x)^2)/2] - b^2*d^2*Pi*x^2*Sin[(Pi*(a + b*x)^2)/2])/(3*b^3*Pi^2)","A",1
130,1,74,122,0.2843456,"\int (c+d x) C(a+b x) \, dx","Integrate[(c + d*x)*FresnelC[a + b*x],x]","\frac{-\pi  (a+b x) C(a+b x) (a d-b (2 c+d x))+\sin \left(\frac{1}{2} \pi  (a+b x)^2\right) (a d-2 b c-b d x)+d S(a+b x)}{2 \pi  b^2}","-\frac{(b c-a d)^2 C(a+b x)}{2 b^2 d}-\frac{(b c-a d) \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b^2}+\frac{d S(a+b x)}{2 \pi  b^2}-\frac{d (a+b x) \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{2 \pi  b^2}+\frac{(c+d x)^2 C(a+b x)}{2 d}",1,"(-(Pi*(a + b*x)*(a*d - b*(2*c + d*x))*FresnelC[a + b*x]) + d*FresnelS[a + b*x] + (-2*b*c + a*d - b*d*x)*Sin[(Pi*(a + b*x)^2)/2])/(2*b^2*Pi)","A",1
131,1,90,37,0.0387029,"\int C(a+b x) \, dx","Integrate[FresnelC[a + b*x],x]","-\frac{\sin \left(\frac{\pi  a^2}{2}\right) \cos \left(\pi  a b x+\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b}-\frac{\cos \left(\frac{\pi  a^2}{2}\right) \sin \left(\pi  a b x+\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b}+x C(a+b x)+\frac{a C(a+b x)}{b}","\frac{(a+b x) C(a+b x)}{b}-\frac{\sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b}",1,"(a*FresnelC[a + b*x])/b + x*FresnelC[a + b*x] - (Cos[a*b*Pi*x + (b^2*Pi*x^2)/2]*Sin[(a^2*Pi)/2])/(b*Pi) - (Cos[(a^2*Pi)/2]*Sin[a*b*Pi*x + (b^2*Pi*x^2)/2])/(b*Pi)","B",1
132,0,0,17,0.0318073,"\int \frac{C(a+b x)}{c+d x} \, dx","Integrate[FresnelC[a + b*x]/(c + d*x),x]","\int \frac{C(a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{C(a+b x)}{c+d x},x\right)",0,"Integrate[FresnelC[a + b*x]/(c + d*x), x]","A",-1
133,0,0,17,2.5362432,"\int \frac{C(a+b x)}{(c+d x)^2} \, dx","Integrate[FresnelC[a + b*x]/(c + d*x)^2,x]","\int \frac{C(a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{C(a+b x)}{(c+d x)^2},x\right)",0,"Integrate[FresnelC[a + b*x]/(c + d*x)^2, x]","A",-1
134,1,166,227,0.3734689,"\int x^3 C(a+b x) \, dx","Integrate[x^3*FresnelC[a + b*x],x]","\frac{\left(-\pi ^2 a^4+\pi ^2 b^4 x^4+3\right) C(a+b x)+\pi  a^3 \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)+6 \pi  a^2 S(a+b x)-\pi  a^2 b x \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)-\pi  b^3 x^3 \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)+\pi  a b^2 x^2 \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)+5 a \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)-3 b x \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{4 \pi ^2 b^4}","-\frac{a^4 C(a+b x)}{4 b^4}+\frac{a^3 \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b^4}+\frac{3 a^2 S(a+b x)}{2 \pi  b^4}-\frac{3 a^2 (a+b x) \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{2 \pi  b^4}+\frac{3 C(a+b x)}{4 \pi ^2 b^4}+\frac{a (a+b x)^2 \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b^4}-\frac{(a+b x)^3 \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{4 \pi  b^4}+\frac{2 a \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi ^2 b^4}-\frac{3 (a+b x) \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{4 \pi ^2 b^4}+\frac{1}{4} x^4 C(a+b x)",1,"(5*a*Cos[(Pi*(a + b*x)^2)/2] - 3*b*x*Cos[(Pi*(a + b*x)^2)/2] + (3 - a^4*Pi^2 + b^4*Pi^2*x^4)*FresnelC[a + b*x] + 6*a^2*Pi*FresnelS[a + b*x] + a^3*Pi*Sin[(Pi*(a + b*x)^2)/2] - a^2*b*Pi*x*Sin[(Pi*(a + b*x)^2)/2] + a*b^2*Pi*x^2*Sin[(Pi*(a + b*x)^2)/2] - b^3*Pi*x^3*Sin[(Pi*(a + b*x)^2)/2])/(4*b^4*Pi^2)","A",1
135,1,116,148,0.3341803,"\int x^2 C(a+b x) \, dx","Integrate[x^2*FresnelC[a + b*x],x]","-\frac{-\pi ^2 \left(a^3+b^3 x^3\right) C(a+b x)+\pi  a^2 \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)+\pi  b^2 x^2 \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)+3 \pi  a S(a+b x)-\pi  a b x \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)+2 \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{3 \pi ^2 b^3}","\frac{a^3 C(a+b x)}{3 b^3}-\frac{a^2 \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b^3}-\frac{a S(a+b x)}{\pi  b^3}+\frac{a (a+b x) \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b^3}-\frac{(a+b x)^2 \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{3 \pi  b^3}-\frac{2 \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{3 \pi ^2 b^3}+\frac{1}{3} x^3 C(a+b x)",1,"-1/3*(2*Cos[(Pi*(a + b*x)^2)/2] - Pi^2*(a^3 + b^3*x^3)*FresnelC[a + b*x] + 3*a*Pi*FresnelS[a + b*x] + a^2*Pi*Sin[(Pi*(a + b*x)^2)/2] - a*b*Pi*x*Sin[(Pi*(a + b*x)^2)/2] + b^2*Pi*x^2*Sin[(Pi*(a + b*x)^2)/2])/(b^3*Pi^2)","A",1
136,1,59,95,0.1794854,"\int x C(a+b x) \, dx","Integrate[x*FresnelC[a + b*x],x]","\frac{\left(\pi  b^2 x^2-\pi  a^2\right) C(a+b x)+S(a+b x)+(a-b x) \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{2 \pi  b^2}","-\frac{a^2 C(a+b x)}{2 b^2}+\frac{S(a+b x)}{2 \pi  b^2}+\frac{a \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b^2}-\frac{(a+b x) \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{2 \pi  b^2}+\frac{1}{2} x^2 C(a+b x)",1,"((-(a^2*Pi) + b^2*Pi*x^2)*FresnelC[a + b*x] + FresnelS[a + b*x] + (a - b*x)*Sin[(Pi*(a + b*x)^2)/2])/(2*b^2*Pi)","A",1
137,1,90,37,0.0371732,"\int C(a+b x) \, dx","Integrate[FresnelC[a + b*x],x]","-\frac{\sin \left(\frac{\pi  a^2}{2}\right) \cos \left(\pi  a b x+\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b}-\frac{\cos \left(\frac{\pi  a^2}{2}\right) \sin \left(\pi  a b x+\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b}+x C(a+b x)+\frac{a C(a+b x)}{b}","\frac{(a+b x) C(a+b x)}{b}-\frac{\sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b}",1,"(a*FresnelC[a + b*x])/b + x*FresnelC[a + b*x] - (Cos[a*b*Pi*x + (b^2*Pi*x^2)/2]*Sin[(a^2*Pi)/2])/(b*Pi) - (Cos[(a^2*Pi)/2]*Sin[a*b*Pi*x + (b^2*Pi*x^2)/2])/(b*Pi)","B",1
138,0,0,13,0.0246055,"\int \frac{C(a+b x)}{x} \, dx","Integrate[FresnelC[a + b*x]/x,x]","\int \frac{C(a+b x)}{x} \, dx","\text{Int}\left(\frac{C(a+b x)}{x},x\right)",0,"Integrate[FresnelC[a + b*x]/x, x]","A",-1
139,0,0,13,1.566885,"\int \frac{C(a+b x)}{x^2} \, dx","Integrate[FresnelC[a + b*x]/x^2,x]","\int \frac{C(a+b x)}{x^2} \, dx","\text{Int}\left(\frac{C(a+b x)}{x^2},x\right)",0,"Integrate[FresnelC[a + b*x]/x^2, x]","A",-1
140,1,253,253,0.0271362,"\int x^7 C(b x)^2 \, dx","Integrate[x^7*FresnelC[b*x]^2,x]","-\frac{105 C(b x)^2}{8 \pi ^4 b^8}-\frac{105 x^2}{16 \pi ^4 b^6}-\frac{x^7 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi  b}+\frac{7 x^6}{48 \pi ^2 b^2}-\frac{x^6 \cos \left(\pi  b^2 x^2\right)}{16 \pi ^2 b^2}-\frac{10 \sin \left(\pi  b^2 x^2\right)}{\pi ^5 b^8}+\frac{105 x C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi ^4 b^7}+\frac{55 x^2 \cos \left(\pi  b^2 x^2\right)}{16 \pi ^4 b^6}+\frac{35 x^3 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi ^3 b^5}+\frac{5 x^4 \sin \left(\pi  b^2 x^2\right)}{8 \pi ^3 b^4}-\frac{7 x^5 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi ^2 b^3}+\frac{1}{8} x^8 C(b x)^2","-\frac{105 C(b x)^2}{8 \pi ^4 b^8}-\frac{105 x^2}{16 \pi ^4 b^6}-\frac{x^7 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi  b}+\frac{7 x^6}{48 \pi ^2 b^2}-\frac{x^6 \cos \left(\pi  b^2 x^2\right)}{16 \pi ^2 b^2}-\frac{10 \sin \left(\pi  b^2 x^2\right)}{\pi ^5 b^8}+\frac{105 x C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi ^4 b^7}+\frac{55 x^2 \cos \left(\pi  b^2 x^2\right)}{16 \pi ^4 b^6}+\frac{35 x^3 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi ^3 b^5}+\frac{5 x^4 \sin \left(\pi  b^2 x^2\right)}{8 \pi ^3 b^4}-\frac{7 x^5 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi ^2 b^3}+\frac{1}{8} x^8 C(b x)^2",1,"(-105*x^2)/(16*b^6*Pi^4) + (7*x^6)/(48*b^2*Pi^2) + (55*x^2*Cos[b^2*Pi*x^2])/(16*b^6*Pi^4) - (x^6*Cos[b^2*Pi*x^2])/(16*b^2*Pi^2) + (105*x*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(4*b^7*Pi^4) - (7*x^5*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(4*b^3*Pi^2) - (105*FresnelC[b*x]^2)/(8*b^8*Pi^4) + (x^8*FresnelC[b*x]^2)/8 + (35*x^3*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(4*b^5*Pi^3) - (x^7*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(4*b*Pi) - (10*Sin[b^2*Pi*x^2])/(b^8*Pi^5) + (5*x^4*Sin[b^2*Pi*x^2])/(8*b^4*Pi^3)","A",1
141,1,170,239,0.2729013,"\int x^6 C(b x)^2 \, dx","Integrate[x^6*FresnelC[b*x]^2,x]","\frac{80 \pi ^4 b^7 x^7 C(b x)^2-160 C(b x) \left(\pi  b^2 x^2 \left(\pi ^2 b^4 x^4-24\right) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)+6 \left(\pi ^2 b^4 x^4-8\right) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)\right)+2 b x \left(2 \left(24 \pi ^2 b^4 x^4+85 \pi  b^2 x^2 \sin \left(\pi  b^2 x^2\right)-960\right)+\left(735-20 \pi ^2 b^4 x^4\right) \cos \left(\pi  b^2 x^2\right)\right)-2655 \sqrt{2} C\left(\sqrt{2} b x\right)}{560 \pi ^4 b^7}","-\frac{531 C\left(\sqrt{2} b x\right)}{56 \sqrt{2} \pi ^4 b^7}-\frac{48 x}{7 \pi ^4 b^6}-\frac{2 x^6 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi  b}+\frac{6 x^5}{35 \pi ^2 b^2}-\frac{x^5 \cos \left(\pi  b^2 x^2\right)}{14 \pi ^2 b^2}+\frac{96 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi ^4 b^7}+\frac{21 x \cos \left(\pi  b^2 x^2\right)}{8 \pi ^4 b^6}+\frac{48 x^2 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi ^3 b^5}+\frac{17 x^3 \sin \left(\pi  b^2 x^2\right)}{28 \pi ^3 b^4}-\frac{12 x^4 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi ^2 b^3}+\frac{1}{7} x^7 C(b x)^2",1,"(80*b^7*Pi^4*x^7*FresnelC[b*x]^2 - 2655*Sqrt[2]*FresnelC[Sqrt[2]*b*x] - 160*FresnelC[b*x]*(6*(-8 + b^4*Pi^2*x^4)*Cos[(b^2*Pi*x^2)/2] + b^2*Pi*x^2*(-24 + b^4*Pi^2*x^4)*Sin[(b^2*Pi*x^2)/2]) + 2*b*x*((735 - 20*b^4*Pi^2*x^4)*Cos[b^2*Pi*x^2] + 2*(-960 + 24*b^4*Pi^2*x^4 + 85*b^2*Pi*x^2*Sin[b^2*Pi*x^2])))/(560*b^7*Pi^4)","A",1
142,0,0,265,0.2387982,"\int x^5 C(b x)^2 \, dx","Integrate[x^5*FresnelC[b*x]^2,x]","\int x^5 C(b x)^2 \, dx","-\frac{5 i x^2 \, _2F_2\left(1,1;\frac{3}{2},2;-\frac{1}{2} i b^2 \pi  x^2\right)}{8 \pi ^3 b^4}+\frac{5 i x^2 \, _2F_2\left(1,1;\frac{3}{2},2;\frac{1}{2} i b^2 \pi  x^2\right)}{8 \pi ^3 b^4}-\frac{5 C(b x) S(b x)}{2 \pi ^3 b^6}-\frac{x^5 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 \pi  b}+\frac{5 x^4}{24 \pi ^2 b^2}-\frac{x^4 \cos \left(\pi  b^2 x^2\right)}{12 \pi ^2 b^2}+\frac{11 \cos \left(\pi  b^2 x^2\right)}{6 \pi ^4 b^6}+\frac{5 x C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^5}+\frac{7 x^2 \sin \left(\pi  b^2 x^2\right)}{12 \pi ^3 b^4}-\frac{5 x^3 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 \pi ^2 b^3}+\frac{1}{6} x^6 C(b x)^2",1,"Integrate[x^5*FresnelC[b*x]^2, x]","F",-1
143,1,137,177,0.1555344,"\int x^4 C(b x)^2 \, dx","Integrate[x^4*FresnelC[b*x]^2,x]","\frac{24 \pi ^3 b^5 x^5 C(b x)^2+32 \pi  b^3 x^3+66 b x \sin \left(\pi  b^2 x^2\right)-48 C(b x) \left(4 \pi  b^2 x^2 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)+\left(\pi ^2 b^4 x^4-8\right) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)\right)-12 \pi  b^3 x^3 \cos \left(\pi  b^2 x^2\right)-129 \sqrt{2} S\left(\sqrt{2} b x\right)}{120 \pi ^3 b^5}","-\frac{43 S\left(\sqrt{2} b x\right)}{20 \sqrt{2} \pi ^3 b^5}-\frac{2 x^4 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 \pi  b}+\frac{4 x^3}{15 \pi ^2 b^2}-\frac{x^3 \cos \left(\pi  b^2 x^2\right)}{10 \pi ^2 b^2}+\frac{16 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 \pi ^3 b^5}+\frac{11 x \sin \left(\pi  b^2 x^2\right)}{20 \pi ^3 b^4}-\frac{8 x^2 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 \pi ^2 b^3}+\frac{1}{5} x^5 C(b x)^2",1,"(32*b^3*Pi*x^3 - 12*b^3*Pi*x^3*Cos[b^2*Pi*x^2] + 24*b^5*Pi^3*x^5*FresnelC[b*x]^2 - 129*Sqrt[2]*FresnelS[Sqrt[2]*b*x] - 48*FresnelC[b*x]*(4*b^2*Pi*x^2*Cos[(b^2*Pi*x^2)/2] + (-8 + b^4*Pi^2*x^4)*Sin[(b^2*Pi*x^2)/2]) + 66*b*x*Sin[b^2*Pi*x^2])/(120*b^5*Pi^3)","A",1
144,1,140,140,0.0086047,"\int x^3 C(b x)^2 \, dx","Integrate[x^3*FresnelC[b*x]^2,x]","\frac{3 C(b x)^2}{4 \pi ^2 b^4}-\frac{x^3 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{2 \pi  b}+\frac{3 x^2}{8 \pi ^2 b^2}-\frac{x^2 \cos \left(\pi  b^2 x^2\right)}{8 \pi ^2 b^2}+\frac{\sin \left(\pi  b^2 x^2\right)}{2 \pi ^3 b^4}-\frac{3 x C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{2 \pi ^2 b^3}+\frac{1}{4} x^4 C(b x)^2","\frac{3 C(b x)^2}{4 \pi ^2 b^4}-\frac{x^3 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{2 \pi  b}+\frac{3 x^2}{8 \pi ^2 b^2}-\frac{x^2 \cos \left(\pi  b^2 x^2\right)}{8 \pi ^2 b^2}+\frac{\sin \left(\pi  b^2 x^2\right)}{2 \pi ^3 b^4}-\frac{3 x C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{2 \pi ^2 b^3}+\frac{1}{4} x^4 C(b x)^2",1,"(3*x^2)/(8*b^2*Pi^2) - (x^2*Cos[b^2*Pi*x^2])/(8*b^2*Pi^2) - (3*x*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(2*b^3*Pi^2) + (3*FresnelC[b*x]^2)/(4*b^4*Pi^2) + (x^4*FresnelC[b*x]^2)/4 - (x^3*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(2*b*Pi) + Sin[b^2*Pi*x^2]/(2*b^4*Pi^3)","A",1
145,1,100,124,0.093728,"\int x^2 C(b x)^2 \, dx","Integrate[x^2*FresnelC[b*x]^2,x]","\frac{4 \pi ^2 b^3 x^3 C(b x)^2-8 C(b x) \left(\pi  b^2 x^2 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)+2 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)\right)-2 b x \left(\cos \left(\pi  b^2 x^2\right)-4\right)+5 \sqrt{2} C\left(\sqrt{2} b x\right)}{12 \pi ^2 b^3}","\frac{5 C\left(\sqrt{2} b x\right)}{6 \sqrt{2} \pi ^2 b^3}-\frac{2 x^2 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 \pi  b}-\frac{x \cos \left(\pi  b^2 x^2\right)}{6 \pi ^2 b^2}+\frac{2 x}{3 \pi ^2 b^2}-\frac{4 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 \pi ^2 b^3}+\frac{1}{3} x^3 C(b x)^2",1,"(-2*b*x*(-4 + Cos[b^2*Pi*x^2]) + 4*b^3*Pi^2*x^3*FresnelC[b*x]^2 + 5*Sqrt[2]*FresnelC[Sqrt[2]*b*x] - 8*FresnelC[b*x]*(2*Cos[(b^2*Pi*x^2)/2] + b^2*Pi*x^2*Sin[(b^2*Pi*x^2)/2]))/(12*b^3*Pi^2)","A",1
146,0,0,144,0.1982088,"\int x C(b x)^2 \, dx","Integrate[x*FresnelC[b*x]^2,x]","\int x C(b x)^2 \, dx","\frac{i x^2 \, _2F_2\left(1,1;\frac{3}{2},2;-\frac{1}{2} i b^2 \pi  x^2\right)}{8 \pi }-\frac{i x^2 \, _2F_2\left(1,1;\frac{3}{2},2;\frac{1}{2} i b^2 \pi  x^2\right)}{8 \pi }+\frac{C(b x) S(b x)}{2 \pi  b^2}-\frac{x C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b}-\frac{\cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^2}+\frac{1}{2} x^2 C(b x)^2",1,"Integrate[x*FresnelC[b*x]^2, x]","F",-1
147,1,54,54,0.0130449,"\int C(b x)^2 \, dx","Integrate[FresnelC[b*x]^2,x]","-\frac{2 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b}+x C(b x)^2+\frac{S\left(\sqrt{2} b x\right)}{\sqrt{2} \pi  b}","-\frac{2 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b}+x C(b x)^2+\frac{S\left(\sqrt{2} b x\right)}{\sqrt{2} \pi  b}",1,"x*FresnelC[b*x]^2 + FresnelS[Sqrt[2]*b*x]/(Sqrt[2]*b*Pi) - (2*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(b*Pi)","A",1
148,0,0,13,0.0234122,"\int \frac{C(b x)^2}{x} \, dx","Integrate[FresnelC[b*x]^2/x,x]","\int \frac{C(b x)^2}{x} \, dx","\text{Int}\left(\frac{C(b x)^2}{x},x\right)",0,"Integrate[FresnelC[b*x]^2/x, x]","A",-1
149,0,0,38,0.0279576,"\int \frac{C(b x)^2}{x^2} \, dx","Integrate[FresnelC[b*x]^2/x^2,x]","\int \frac{C(b x)^2}{x^2} \, dx","2 b \text{Int}\left(\frac{C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)-\frac{C(b x)^2}{x}",0,"Integrate[FresnelC[b*x]^2/x^2, x]","A",-1
150,0,0,39,0.019891,"\int \frac{C(b x)^2}{x^3} \, dx","Integrate[FresnelC[b*x]^2/x^3,x]","\int \frac{C(b x)^2}{x^3} \, dx","b \text{Int}\left(\frac{C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x^2},x\right)-\frac{C(b x)^2}{2 x^2}",0,"Integrate[FresnelC[b*x]^2/x^3, x]","A",-1
151,0,0,120,0.0280424,"\int \frac{C(b x)^2}{x^4} \, dx","Integrate[FresnelC[b*x]^2/x^4,x]","\int \frac{C(b x)^2}{x^4} \, dx","-\frac{1}{3} \pi  b^3 \text{Int}\left(\frac{C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)-\frac{\pi  b^3 S\left(\sqrt{2} b x\right)}{3 \sqrt{2}}-\frac{b C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 x^2}-\frac{b^2 \cos \left(\pi  b^2 x^2\right)}{6 x}-\frac{b^2}{6 x}-\frac{C(b x)^2}{3 x^3}",0,"Integrate[FresnelC[b*x]^2/x^4, x]","A",-1
152,1,127,127,0.00957,"\int \frac{C(b x)^2}{x^5} \, dx","Integrate[FresnelC[b*x]^2/x^5,x]","-\frac{1}{12} \pi ^2 b^4 C(b x)^2-\frac{b C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 x^3}-\frac{b^2}{24 x^2}-\frac{b^2 \cos \left(\pi  b^2 x^2\right)}{24 x^2}-\frac{1}{12} \pi  b^4 \text{Si}\left(b^2 \pi  x^2\right)+\frac{\pi  b^3 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 x}-\frac{C(b x)^2}{4 x^4}","-\frac{1}{12} \pi ^2 b^4 C(b x)^2-\frac{b C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 x^3}-\frac{b^2}{24 x^2}-\frac{b^2 \cos \left(\pi  b^2 x^2\right)}{24 x^2}-\frac{1}{12} \pi  b^4 \text{Si}\left(b^2 \pi  x^2\right)+\frac{\pi  b^3 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 x}-\frac{C(b x)^2}{4 x^4}",1,"-1/24*b^2/x^2 - (b^2*Cos[b^2*Pi*x^2])/(24*x^2) - (b*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(6*x^3) - (b^4*Pi^2*FresnelC[b*x]^2)/12 - FresnelC[b*x]^2/(4*x^4) + (b^3*Pi*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(6*x) - (b^4*Pi*SinIntegral[b^2*Pi*x^2])/12","A",1
153,0,0,171,0.0318398,"\int \frac{C(b x)^2}{x^6} \, dx","Integrate[FresnelC[b*x]^2/x^6,x]","\int \frac{C(b x)^2}{x^6} \, dx","-\frac{1}{20} \pi ^2 b^5 \text{Int}\left(\frac{C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)-\frac{7 \pi ^2 b^5 C\left(\sqrt{2} b x\right)}{60 \sqrt{2}}-\frac{b C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{10 x^4}-\frac{b^2}{60 x^3}-\frac{b^2 \cos \left(\pi  b^2 x^2\right)}{60 x^3}+\frac{7 \pi  b^4 \sin \left(\pi  b^2 x^2\right)}{120 x}+\frac{\pi  b^3 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{20 x^2}-\frac{C(b x)^2}{5 x^5}",0,"Integrate[FresnelC[b*x]^2/x^6, x]","A",-1
154,0,0,166,0.0333997,"\int \frac{C(b x)^2}{x^7} \, dx","Integrate[FresnelC[b*x]^2/x^7,x]","\int \frac{C(b x)^2}{x^7} \, dx","-\frac{1}{45} \pi ^2 b^5 \text{Int}\left(\frac{C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x^2},x\right)-\frac{b C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{15 x^5}-\frac{b^2}{120 x^4}-\frac{b^2 \cos \left(\pi  b^2 x^2\right)}{120 x^4}-\frac{1}{72} \pi ^2 b^6 \text{Ci}\left(b^2 \pi  x^2\right)+\frac{\pi  b^4 \sin \left(\pi  b^2 x^2\right)}{72 x^2}+\frac{\pi  b^3 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{45 x^3}-\frac{C(b x)^2}{6 x^6}",0,"Integrate[FresnelC[b*x]^2/x^7, x]","A",-1
155,0,0,259,0.0321469,"\int \frac{C(b x)^2}{x^8} \, dx","Integrate[FresnelC[b*x]^2/x^8,x]","\int \frac{C(b x)^2}{x^8} \, dx","\frac{1}{168} \pi ^3 b^7 \text{Int}\left(\frac{C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)+\frac{2}{315} \sqrt{2} \pi ^3 b^7 S\left(\sqrt{2} b x\right)+\frac{\pi ^3 b^7 S\left(\sqrt{2} b x\right)}{72 \sqrt{2}}+\frac{\pi ^2 b^6}{336 x}-\frac{b C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{21 x^6}-\frac{b^2}{210 x^5}-\frac{b^2 \cos \left(\pi  b^2 x^2\right)}{210 x^5}+\frac{67 \pi ^2 b^6 \cos \left(\pi  b^2 x^2\right)}{5040 x}+\frac{\pi ^2 b^5 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{168 x^2}+\frac{13 \pi  b^4 \sin \left(\pi  b^2 x^2\right)}{2520 x^3}+\frac{\pi  b^3 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{84 x^4}-\frac{C(b x)^2}{7 x^7}",0,"Integrate[FresnelC[b*x]^2/x^8, x]","A",-1
156,1,242,242,0.024083,"\int \frac{C(b x)^2}{x^9} \, dx","Integrate[FresnelC[b*x]^2/x^9,x]","\frac{1}{840} \pi ^4 b^8 C(b x)^2+\frac{\pi ^2 b^6}{1680 x^2}-\frac{b C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{28 x^7}-\frac{b^2}{336 x^6}-\frac{b^2 \cos \left(\pi  b^2 x^2\right)}{336 x^6}+\frac{1}{280} \pi ^3 b^8 \text{Si}\left(b^2 \pi  x^2\right)-\frac{\pi ^3 b^7 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{420 x}+\frac{\pi ^2 b^6 \cos \left(\pi  b^2 x^2\right)}{336 x^2}+\frac{\pi ^2 b^5 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{420 x^3}+\frac{\pi  b^4 \sin \left(\pi  b^2 x^2\right)}{420 x^4}+\frac{\pi  b^3 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{140 x^5}-\frac{C(b x)^2}{8 x^8}","\frac{1}{840} \pi ^4 b^8 C(b x)^2+\frac{\pi ^2 b^6}{1680 x^2}-\frac{b C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{28 x^7}-\frac{b^2}{336 x^6}-\frac{b^2 \cos \left(\pi  b^2 x^2\right)}{336 x^6}+\frac{1}{280} \pi ^3 b^8 \text{Si}\left(b^2 \pi  x^2\right)-\frac{\pi ^3 b^7 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{420 x}+\frac{\pi ^2 b^6 \cos \left(\pi  b^2 x^2\right)}{336 x^2}+\frac{\pi ^2 b^5 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{420 x^3}+\frac{\pi  b^4 \sin \left(\pi  b^2 x^2\right)}{420 x^4}+\frac{\pi  b^3 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{140 x^5}-\frac{C(b x)^2}{8 x^8}",1,"-1/336*b^2/x^6 + (b^6*Pi^2)/(1680*x^2) - (b^2*Cos[b^2*Pi*x^2])/(336*x^6) + (b^6*Pi^2*Cos[b^2*Pi*x^2])/(336*x^2) - (b*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(28*x^7) + (b^5*Pi^2*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(420*x^3) + (b^8*Pi^4*FresnelC[b*x]^2)/840 - FresnelC[b*x]^2/(8*x^8) + (b^3*Pi*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(140*x^5) - (b^7*Pi^3*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(420*x) + (b^4*Pi*Sin[b^2*Pi*x^2])/(420*x^4) + (b^8*Pi^3*SinIntegral[b^2*Pi*x^2])/280","A",1
157,0,0,286,0.0342136,"\int \frac{C(b x)^2}{x^{10}} \, dx","Integrate[FresnelC[b*x]^2/x^10,x]","\int \frac{C(b x)^2}{x^{10}} \, dx","\frac{\pi ^4 b^9 \text{Int}\left(\frac{C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)}{1728}+\frac{853 \pi ^4 b^9 C\left(\sqrt{2} b x\right)}{181440 \sqrt{2}}+\frac{\pi ^2 b^6}{5184 x^3}-\frac{b C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{36 x^8}-\frac{b^2}{504 x^7}-\frac{b^2 \cos \left(\pi  b^2 x^2\right)}{504 x^7}-\frac{853 \pi ^3 b^8 \sin \left(\pi  b^2 x^2\right)}{362880 x}-\frac{\pi ^3 b^7 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{1728 x^2}+\frac{187 \pi ^2 b^6 \cos \left(\pi  b^2 x^2\right)}{181440 x^3}+\frac{\pi ^2 b^5 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{864 x^4}+\frac{19 \pi  b^4 \sin \left(\pi  b^2 x^2\right)}{15120 x^5}+\frac{\pi  b^3 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{216 x^6}-\frac{C(b x)^2}{9 x^9}",0,"Integrate[FresnelC[b*x]^2/x^10, x]","A",-1
158,0,0,495,0.817483,"\int (c+d x)^2 C(a+b x)^2 \, dx","Integrate[(c + d*x)^2*FresnelC[a + b*x]^2,x]","\int (c+d x)^2 C(a+b x)^2 \, dx","\frac{i d (a+b x)^2 (b c-a d) \, _2F_2\left(1,1;\frac{3}{2},2;-\frac{1}{2} i \pi  (a+b x)^2\right)}{4 \pi  b^3}-\frac{i d (a+b x)^2 (b c-a d) \, _2F_2\left(1,1;\frac{3}{2},2;\frac{1}{2} i \pi  (a+b x)^2\right)}{4 \pi  b^3}+\frac{d (b c-a d) C(a+b x) S(a+b x)}{\pi  b^3}+\frac{d (a+b x)^2 (b c-a d) C(a+b x)^2}{b^3}+\frac{(a+b x) (b c-a d)^2 C(a+b x)^2}{b^3}-\frac{2 d (a+b x) (b c-a d) C(a+b x) \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b^3}-\frac{2 (b c-a d)^2 C(a+b x) \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b^3}+\frac{(b c-a d)^2 S\left(\sqrt{2} (a+b x)\right)}{\sqrt{2} \pi  b^3}-\frac{d (b c-a d) \cos \left(\pi  (a+b x)^2\right)}{2 \pi ^2 b^3}+\frac{d^2 (a+b x)^3 C(a+b x)^2}{3 b^3}+\frac{5 d^2 C\left(\sqrt{2} (a+b x)\right)}{6 \sqrt{2} \pi ^2 b^3}-\frac{2 d^2 (a+b x)^2 C(a+b x) \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{3 \pi  b^3}-\frac{4 d^2 C(a+b x) \cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{3 \pi ^2 b^3}-\frac{d^2 (a+b x) \cos \left(\pi  (a+b x)^2\right)}{6 \pi ^2 b^3}+\frac{2 d^2 x}{3 \pi ^2 b^2}",1,"Integrate[(c + d*x)^2*FresnelC[a + b*x]^2, x]","F",-1
159,0,0,279,0.6812921,"\int (c+d x) C(a+b x)^2 \, dx","Integrate[(c + d*x)*FresnelC[a + b*x]^2,x]","\int (c+d x) C(a+b x)^2 \, dx","\frac{i d (a+b x)^2 \, _2F_2\left(1,1;\frac{3}{2},2;-\frac{1}{2} i \pi  (a+b x)^2\right)}{8 \pi  b^2}-\frac{i d (a+b x)^2 \, _2F_2\left(1,1;\frac{3}{2},2;\frac{1}{2} i \pi  (a+b x)^2\right)}{8 \pi  b^2}+\frac{(a+b x) (b c-a d) C(a+b x)^2}{b^2}-\frac{2 (b c-a d) C(a+b x) \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b^2}+\frac{(b c-a d) S\left(\sqrt{2} (a+b x)\right)}{\sqrt{2} \pi  b^2}+\frac{d C(a+b x) S(a+b x)}{2 \pi  b^2}+\frac{d (a+b x)^2 C(a+b x)^2}{2 b^2}-\frac{d (a+b x) C(a+b x) \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b^2}-\frac{d \cos \left(\pi  (a+b x)^2\right)}{4 \pi ^2 b^2}",1,"Integrate[(c + d*x)*FresnelC[a + b*x]^2, x]","F",-1
160,1,66,69,0.0184959,"\int C(a+b x)^2 \, dx","Integrate[FresnelC[a + b*x]^2,x]","\frac{2 \pi  (a+b x) C(a+b x)^2-4 C(a+b x) \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)+\sqrt{2} S\left(\sqrt{2} (a+b x)\right)}{2 \pi  b}","\frac{(a+b x) C(a+b x)^2}{b}-\frac{2 C(a+b x) \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b}+\frac{S\left(\sqrt{2} (a+b x)\right)}{\sqrt{2} \pi  b}",1,"(2*Pi*(a + b*x)*FresnelC[a + b*x]^2 + Sqrt[2]*FresnelS[Sqrt[2]*(a + b*x)] - 4*FresnelC[a + b*x]*Sin[(Pi*(a + b*x)^2)/2])/(2*b*Pi)","A",1
161,0,0,19,0.0390583,"\int \frac{C(a+b x)^2}{c+d x} \, dx","Integrate[FresnelC[a + b*x]^2/(c + d*x),x]","\int \frac{C(a+b x)^2}{c+d x} \, dx","\text{Int}\left(\frac{C(a+b x)^2}{c+d x},x\right)",0,"Integrate[FresnelC[a + b*x]^2/(c + d*x), x]","A",-1
162,0,0,19,0.0900592,"\int \frac{C(a+b x)^2}{(c+d x)^2} \, dx","Integrate[FresnelC[a + b*x]^2/(c + d*x)^2,x]","\int \frac{C(a+b x)^2}{(c+d x)^2} \, dx","\text{Int}\left(\frac{C(a+b x)^2}{(c+d x)^2},x\right)",0,"Integrate[FresnelC[a + b*x]^2/(c + d*x)^2, x]","A",-1
163,1,318,231,7.6807137,"\int x^2 C\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[x^2*FresnelC[d*(a + b*Log[c*x^n])],x]","\frac{1}{12} x^3 \left(4 C\left(d \left(a+b \log \left(c x^n\right)\right)\right)+\sqrt[4]{-1} \sqrt{2} \left(c x^n\right)^{-3/n} \left(i e^{\frac{9 i}{\pi  b^2 d^2 n^2}} \text{erfi}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(\pi  a b d^2 n+\pi  b^2 d^2 n \log \left(c x^n\right)-3 i\right)}{\sqrt{\pi } b d n}\right)+\text{erfi}\left(\frac{(-1)^{3/4} \left(\pi  a b d^2 n+\pi  b^2 d^2 n \log \left(c x^n\right)+3 i\right)}{\sqrt{2 \pi } b d n}\right)\right) \exp \left(\frac{1}{2} \left(-i \pi  a^2 d^2+2 i \pi  a b d^2 \left(n \log (x)-\log \left(c x^n\right)\right)-\frac{6 a}{b n}-i \pi  b^2 d^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2-\frac{9 i}{\pi  b^2 d^2 n^2}\right)\right) \left(\cos \left(\frac{1}{2} \pi  d^2 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)^2\right)+i \sin \left(\frac{1}{2} \pi  d^2 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)^2\right)\right)\right)","\left(\frac{1}{12}+\frac{i}{12}\right) x^3 \left(c x^n\right)^{-3/n} e^{-\frac{3 a}{b n}+\frac{9 i}{2 \pi  b^2 d^2 n^2}} \text{erf}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(i \pi  a b d^2+i \pi  b^2 d^2 \log \left(c x^n\right)+\frac{3}{n}\right)}{\sqrt{\pi } b d}\right)-\left(\frac{1}{12}+\frac{i}{12}\right) x^3 \left(c x^n\right)^{-3/n} e^{-\frac{3 a}{b n}-\frac{9 i}{2 \pi  b^2 d^2 n^2}} \text{erfi}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(-i \pi  a b d^2-i \pi  b^2 d^2 \log \left(c x^n\right)+\frac{3}{n}\right)}{\sqrt{\pi } b d}\right)+\frac{1}{3} x^3 C\left(d \left(a+b \log \left(c x^n\right)\right)\right)",1,"(x^3*(4*FresnelC[d*(a + b*Log[c*x^n])] + ((-1)^(1/4)*Sqrt[2]*E^(((-6*a)/(b*n) - (9*I)/(b^2*d^2*n^2*Pi) - I*a^2*d^2*Pi + (2*I)*a*b*d^2*Pi*(n*Log[x] - Log[c*x^n]) - I*b^2*d^2*Pi*(-(n*Log[x]) + Log[c*x^n])^2)/2)*(I*E^((9*I)/(b^2*d^2*n^2*Pi))*Erfi[((1/2 + I/2)*(-3*I + a*b*d^2*n*Pi + b^2*d^2*n*Pi*Log[c*x^n]))/(b*d*n*Sqrt[Pi])] + Erfi[((-1)^(3/4)*(3*I + a*b*d^2*n*Pi + b^2*d^2*n*Pi*Log[c*x^n]))/(b*d*n*Sqrt[2*Pi])])*(Cos[(d^2*Pi*(a - b*n*Log[x] + b*Log[c*x^n])^2)/2] + I*Sin[(d^2*Pi*(a - b*n*Log[x] + b*Log[c*x^n])^2)/2]))/(c*x^n)^(3/n)))/12","A",0
164,1,318,227,7.5418383,"\int x C\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[x*FresnelC[d*(a + b*Log[c*x^n])],x]","\frac{1}{8} x^2 \left(4 C\left(d \left(a+b \log \left(c x^n\right)\right)\right)+\sqrt[4]{-1} \sqrt{2} \left(c x^n\right)^{-2/n} \left(i e^{\frac{4 i}{\pi  b^2 d^2 n^2}} \text{erfi}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(\pi  a b d^2 n+\pi  b^2 d^2 n \log \left(c x^n\right)-2 i\right)}{\sqrt{\pi } b d n}\right)+\text{erfi}\left(\frac{(-1)^{3/4} \left(\pi  a b d^2 n+\pi  b^2 d^2 n \log \left(c x^n\right)+2 i\right)}{\sqrt{2 \pi } b d n}\right)\right) \exp \left(-\frac{1}{2} i \pi  a^2 d^2+i \pi  a b d^2 \left(n \log (x)-\log \left(c x^n\right)\right)-\frac{2 a}{b n}-\frac{1}{2} i \pi  b^2 d^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2-\frac{2 i}{\pi  b^2 d^2 n^2}\right) \left(\cos \left(\frac{1}{2} \pi  d^2 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)^2\right)+i \sin \left(\frac{1}{2} \pi  d^2 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)^2\right)\right)\right)","\left(\frac{1}{8}+\frac{i}{8}\right) x^2 \left(c x^n\right)^{-2/n} e^{\frac{-2 \pi  a b d^2 n+2 i}{\pi  b^2 d^2 n^2}} \text{erf}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(i \pi  a b d^2+i \pi  b^2 d^2 \log \left(c x^n\right)+\frac{2}{n}\right)}{\sqrt{\pi } b d}\right)-\left(\frac{1}{8}+\frac{i}{8}\right) x^2 \left(c x^n\right)^{-2/n} e^{-\frac{2 \left(\pi  a b d^2 n+i\right)}{\pi  b^2 d^2 n^2}} \text{erfi}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(-i \pi  a b d^2-i \pi  b^2 d^2 \log \left(c x^n\right)+\frac{2}{n}\right)}{\sqrt{\pi } b d}\right)+\frac{1}{2} x^2 C\left(d \left(a+b \log \left(c x^n\right)\right)\right)",1,"(x^2*(4*FresnelC[d*(a + b*Log[c*x^n])] + ((-1)^(1/4)*Sqrt[2]*E^((-2*a)/(b*n) - (2*I)/(b^2*d^2*n^2*Pi) - (I/2)*a^2*d^2*Pi + I*a*b*d^2*Pi*(n*Log[x] - Log[c*x^n]) - (I/2)*b^2*d^2*Pi*(-(n*Log[x]) + Log[c*x^n])^2)*(I*E^((4*I)/(b^2*d^2*n^2*Pi))*Erfi[((1/2 + I/2)*(-2*I + a*b*d^2*n*Pi + b^2*d^2*n*Pi*Log[c*x^n]))/(b*d*n*Sqrt[Pi])] + Erfi[((-1)^(3/4)*(2*I + a*b*d^2*n*Pi + b^2*d^2*n*Pi*Log[c*x^n]))/(b*d*n*Sqrt[2*Pi])])*(Cos[(d^2*Pi*(a - b*n*Log[x] + b*Log[c*x^n])^2)/2] + I*Sin[(d^2*Pi*(a - b*n*Log[x] + b*Log[c*x^n])^2)/2]))/(c*x^n)^(2/n)))/8","A",0
165,1,315,214,7.4641224,"\int C\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[FresnelC[d*(a + b*Log[c*x^n])],x]","x C\left(d \left(a+b \log \left(c x^n\right)\right)\right)+\frac{\sqrt[4]{-1} x \left(c x^n\right)^{-1/n} \left(i e^{\frac{i}{\pi  b^2 d^2 n^2}} \text{erfi}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(\pi  a b d^2 n+\pi  b^2 d^2 n \log \left(c x^n\right)-i\right)}{\sqrt{\pi } b d n}\right)+\text{erfi}\left(\frac{(-1)^{3/4} \left(\pi  a b d^2 n+\pi  b^2 d^2 n \log \left(c x^n\right)+i\right)}{\sqrt{2 \pi } b d n}\right)\right) \exp \left(\frac{1}{2} \left(-i \pi  a^2 d^2+2 i \pi  a b d^2 \left(n \log (x)-\log \left(c x^n\right)\right)-\frac{2 a}{b n}-i \pi  b^2 d^2 \left(\log \left(c x^n\right)-n \log (x)\right)^2-\frac{i}{\pi  b^2 d^2 n^2}\right)\right) \left(\cos \left(\frac{1}{2} \pi  d^2 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)^2\right)+i \sin \left(\frac{1}{2} \pi  d^2 \left(a+b \log \left(c x^n\right)-b n \log (x)\right)^2\right)\right)}{2 \sqrt{2}}","\left(\frac{1}{4}+\frac{i}{4}\right) x \left(c x^n\right)^{-1/n} e^{-\frac{2 a b n-\frac{i}{\pi  d^2}}{2 b^2 n^2}} \text{erf}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(i \pi  a b d^2+i \pi  b^2 d^2 \log \left(c x^n\right)+\frac{1}{n}\right)}{\sqrt{\pi } b d}\right)-\left(\frac{1}{4}+\frac{i}{4}\right) x \left(c x^n\right)^{-1/n} e^{-\frac{2 a b n+\frac{i}{\pi  d^2}}{2 b^2 n^2}} \text{erfi}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(-i \pi  a b d^2-i \pi  b^2 d^2 \log \left(c x^n\right)+\frac{1}{n}\right)}{\sqrt{\pi } b d}\right)+x C\left(d \left(a+b \log \left(c x^n\right)\right)\right)",1,"x*FresnelC[d*(a + b*Log[c*x^n])] + ((-1)^(1/4)*E^(((-2*a)/(b*n) - I/(b^2*d^2*n^2*Pi) - I*a^2*d^2*Pi + (2*I)*a*b*d^2*Pi*(n*Log[x] - Log[c*x^n]) - I*b^2*d^2*Pi*(-(n*Log[x]) + Log[c*x^n])^2)/2)*x*(I*E^(I/(b^2*d^2*n^2*Pi))*Erfi[((1/2 + I/2)*(-I + a*b*d^2*n*Pi + b^2*d^2*n*Pi*Log[c*x^n]))/(b*d*n*Sqrt[Pi])] + Erfi[((-1)^(3/4)*(I + a*b*d^2*n*Pi + b^2*d^2*n*Pi*Log[c*x^n]))/(b*d*n*Sqrt[2*Pi])])*(Cos[(d^2*Pi*(a - b*n*Log[x] + b*Log[c*x^n])^2)/2] + I*Sin[(d^2*Pi*(a - b*n*Log[x] + b*Log[c*x^n])^2)/2]))/(2*Sqrt[2]*(c*x^n)^n^(-1))","A",0
166,1,165,66,0.1042113,"\int \frac{C\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x} \, dx","Integrate[FresnelC[d*(a + b*Log[c*x^n])]/x,x]","-\frac{\sin \left(\frac{1}{2} \pi  a^2 d^2\right) \cos \left(\pi  a b d^2 \log \left(c x^n\right)+\frac{1}{2} \pi  b^2 d^2 \log ^2\left(c x^n\right)\right)}{\pi  b d n}-\frac{\cos \left(\frac{1}{2} \pi  a^2 d^2\right) \sin \left(\pi  a b d^2 \log \left(c x^n\right)+\frac{1}{2} \pi  b^2 d^2 \log ^2\left(c x^n\right)\right)}{\pi  b d n}+\frac{\log \left(c x^n\right) C\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{n}+\frac{a C\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{b n}","\frac{\left(a+b \log \left(c x^n\right)\right) C\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{b n}-\frac{\sin \left(\frac{1}{2} \pi  d^2 \left(a+b \log \left(c x^n\right)\right)^2\right)}{\pi  b d n}",1,"(a*FresnelC[d*(a + b*Log[c*x^n])])/(b*n) + (FresnelC[d*(a + b*Log[c*x^n])]*Log[c*x^n])/n - (Cos[a*b*d^2*Pi*Log[c*x^n] + (b^2*d^2*Pi*Log[c*x^n]^2)/2]*Sin[(a^2*d^2*Pi)/2])/(b*d*n*Pi) - (Cos[(a^2*d^2*Pi)/2]*Sin[a*b*d^2*Pi*Log[c*x^n] + (b^2*d^2*Pi*Log[c*x^n]^2)/2])/(b*d*n*Pi)","B",1
167,1,194,217,4.6170433,"\int \frac{C\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^2} \, dx","Integrate[FresnelC[d*(a + b*Log[c*x^n])]/x^2,x]","-\frac{4 C\left(d \left(a+b \log \left(c x^n\right)\right)\right)+\sqrt[4]{-1} \sqrt{2} \left(c x^n\right)^{\frac{1}{n}} e^{\frac{2 a b n-\frac{i}{\pi  d^2}}{2 b^2 n^2}} \left(i e^{\frac{i}{\pi  b^2 d^2 n^2}} \text{erfi}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(\pi  a b d^2 n+\pi  b^2 d^2 n \log \left(c x^n\right)+i\right)}{\sqrt{\pi } b d n}\right)+\text{erfi}\left(\frac{(-1)^{3/4} \left(\pi  a b d^2 n+\pi  b^2 d^2 n \log \left(c x^n\right)-i\right)}{\sqrt{2 \pi } b d n}\right)\right)}{4 x}","\frac{\left(\frac{1}{4}+\frac{i}{4}\right) \left(c x^n\right)^{\frac{1}{n}} e^{\frac{2 a b n+\frac{i}{\pi  d^2}}{2 b^2 n^2}} \text{erf}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(-i \pi  a b d^2-i \pi  b^2 d^2 \log \left(c x^n\right)+\frac{1}{n}\right)}{\sqrt{\pi } b d}\right)}{x}-\frac{\left(\frac{1}{4}+\frac{i}{4}\right) \left(c x^n\right)^{\frac{1}{n}} e^{\frac{2 a b n-\frac{i}{\pi  d^2}}{2 b^2 n^2}} \text{erfi}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(i \pi  a b d^2+i \pi  b^2 d^2 \log \left(c x^n\right)+\frac{1}{n}\right)}{\sqrt{\pi } b d}\right)}{x}-\frac{C\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x}",1,"-1/4*((-1)^(1/4)*Sqrt[2]*E^((2*a*b*n - I/(d^2*Pi))/(2*b^2*n^2))*(c*x^n)^n^(-1)*(Erfi[((-1)^(3/4)*(-I + a*b*d^2*n*Pi + b^2*d^2*n*Pi*Log[c*x^n]))/(b*d*n*Sqrt[2*Pi])] + I*E^(I/(b^2*d^2*n^2*Pi))*Erfi[((1/2 + I/2)*(I + a*b*d^2*n*Pi + b^2*d^2*n*Pi*Log[c*x^n]))/(b*d*n*Sqrt[Pi])]) + 4*FresnelC[d*(a + b*Log[c*x^n])])/x","A",1
168,1,199,228,4.5753221,"\int \frac{C\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^3} \, dx","Integrate[FresnelC[d*(a + b*Log[c*x^n])]/x^3,x]","-\frac{C\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{2 x^2}-\frac{\sqrt[4]{-1} \left(i e^{\frac{4 i}{\pi  b^2 d^2 n^2}} \text{erfi}\left(\frac{\sqrt[4]{-1} \left(\pi  a b d^2 n+\pi  b^2 d^2 n \log \left(c x^n\right)+2 i\right)}{\sqrt{2 \pi } b d n}\right)+\text{erfi}\left(\frac{(-1)^{3/4} \left(\pi  a b d^2 n+\pi  b^2 d^2 n \log \left(c x^n\right)-2 i\right)}{\sqrt{2 \pi } b d n}\right)\right) \exp \left(\frac{2 \left(\frac{a n}{b}-\frac{i}{\pi  b^2 d^2}+n \left(\log \left(c x^n\right)-n \log (x)\right)\right)}{n^2}\right)}{4 \sqrt{2}}","\frac{\left(\frac{1}{8}+\frac{i}{8}\right) \left(c x^n\right)^{2/n} e^{\frac{2 \pi  a b d^2 n+2 i}{\pi  b^2 d^2 n^2}} \text{erf}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(-i \pi  a b d^2-i \pi  b^2 d^2 \log \left(c x^n\right)+\frac{2}{n}\right)}{\sqrt{\pi } b d}\right)}{x^2}-\frac{\left(\frac{1}{8}+\frac{i}{8}\right) \left(c x^n\right)^{2/n} e^{-\frac{2 \left(-\pi  a b d^2 n+i\right)}{\pi  b^2 d^2 n^2}} \text{erfi}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(i \pi  a b d^2+i \pi  b^2 d^2 \log \left(c x^n\right)+\frac{2}{n}\right)}{\sqrt{\pi } b d}\right)}{x^2}-\frac{C\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{2 x^2}",1,"-1/4*((-1)^(1/4)*E^((2*((a*n)/b - I/(b^2*d^2*Pi) + n*(-(n*Log[x]) + Log[c*x^n])))/n^2)*(Erfi[((-1)^(3/4)*(-2*I + a*b*d^2*n*Pi + b^2*d^2*n*Pi*Log[c*x^n]))/(b*d*n*Sqrt[2*Pi])] + I*E^((4*I)/(b^2*d^2*n^2*Pi))*Erfi[((-1)^(1/4)*(2*I + a*b*d^2*n*Pi + b^2*d^2*n*Pi*Log[c*x^n]))/(b*d*n*Sqrt[2*Pi])]))/Sqrt[2] - FresnelC[d*(a + b*Log[c*x^n])]/(2*x^2)","A",1
169,1,244,280,6.0450456,"\int (e x)^m C\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Integrate[(e*x)^m*FresnelC[d*(a + b*Log[c*x^n])],x]","\frac{(e x)^m \left(4 x C\left(d \left(a+b \log \left(c x^n\right)\right)\right)+(-1)^{3/4} \sqrt{2} x^{-m} \exp \left(-\frac{(m+1) \left(2 \pi  a b d^2 n+2 \pi  b^2 d^2 n \left(\log \left(c x^n\right)-n \log (x)\right)+i m+i\right)}{2 \pi  b^2 d^2 n^2}\right) \left(\text{erf}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(\pi  a b d^2 n+\pi  b^2 d^2 n \log \left(c x^n\right)+i m+i\right)}{\sqrt{\pi } b d n}\right)-e^{\frac{i (m+1)^2}{\pi  b^2 d^2 n^2}} \text{erfi}\left(\frac{(-1)^{3/4} \left(i \pi  a b d^2 n+i \pi  b^2 d^2 n \log \left(c x^n\right)+m+1\right)}{\sqrt{2 \pi } b d n}\right)\right)\right)}{4 (m+1)}","\frac{\left(\frac{1}{4}+\frac{i}{4}\right) x (e x)^m \left(c x^n\right)^{-\frac{m+1}{n}} \exp \left(\frac{i (m+1) \left(2 i \pi  a b d^2 n+m+1\right)}{2 \pi  b^2 d^2 n^2}\right) \text{erf}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(i \pi  a b d^2 n+i \pi  b^2 d^2 n \log \left(c x^n\right)+m+1\right)}{\sqrt{\pi } b d n}\right)}{m+1}-\frac{\left(\frac{1}{4}+\frac{i}{4}\right) x (e x)^m \left(c x^n\right)^{-\frac{m+1}{n}} \exp \left(-\frac{i (m+1) \left(-2 i \pi  a b d^2 n+m+1\right)}{2 \pi  b^2 d^2 n^2}\right) \text{erfi}\left(\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \left(-i \pi  a b d^2 n-i \pi  b^2 d^2 n \log \left(c x^n\right)+m+1\right)}{\sqrt{\pi } b d n}\right)}{m+1}+\frac{(e x)^{m+1} C\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e (m+1)}",1,"((e*x)^m*(((-1)^(3/4)*Sqrt[2]*(Erf[((1/2 + I/2)*(I + I*m + a*b*d^2*n*Pi + b^2*d^2*n*Pi*Log[c*x^n]))/(b*d*n*Sqrt[Pi])] - E^((I*(1 + m)^2)/(b^2*d^2*n^2*Pi))*Erfi[((-1)^(3/4)*(1 + m + I*a*b*d^2*n*Pi + I*b^2*d^2*n*Pi*Log[c*x^n]))/(b*d*n*Sqrt[2*Pi])]))/(E^(((1 + m)*(I + I*m + 2*a*b*d^2*n*Pi + 2*b^2*d^2*n*Pi*(-(n*Log[x]) + Log[c*x^n])))/(2*b^2*d^2*n^2*Pi))*x^m) + 4*x*FresnelC[d*(a + b*Log[c*x^n])]))/(4*(1 + m))","A",1
170,0,0,64,0.0461498,"\int e^{c+\frac{1}{2} i b^2 \pi  x^2} C(b x) \, dx","Integrate[E^(c + (I/2)*b^2*Pi*x^2)*FresnelC[b*x],x]","\int e^{c+\frac{1}{2} i b^2 \pi  x^2} C(b x) \, dx","\frac{1}{4} b e^c x^2 \, _2F_2\left(1,1;\frac{3}{2},2;\frac{1}{2} i b^2 \pi  x^2\right)-\frac{i e^c \text{erfi}\left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\pi } b x\right)^2}{8 b}",1,"Integrate[E^(c + (I/2)*b^2*Pi*x^2)*FresnelC[b*x], x]","F",-1
171,0,0,64,0.0382066,"\int e^{c-\frac{1}{2} i b^2 \pi  x^2} C(b x) \, dx","Integrate[E^(c - (I/2)*b^2*Pi*x^2)*FresnelC[b*x],x]","\int e^{c-\frac{1}{2} i b^2 \pi  x^2} C(b x) \, dx","\frac{1}{4} b e^c x^2 \, _2F_2\left(1,1;\frac{3}{2},2;-\frac{1}{2} i b^2 \pi  x^2\right)-\frac{i e^c \text{erf}\left(\left(\frac{1}{2}+\frac{i}{2}\right) \sqrt{\pi } b x\right)^2}{8 b}",1,"Integrate[E^(c - (I/2)*b^2*Pi*x^2)*FresnelC[b*x], x]","F",-1
172,0,0,101,0.0437402,"\int C(b x) \sin \left(c+\frac{1}{2} b^2 \pi  x^2\right) \, dx","Integrate[FresnelC[b*x]*Sin[c + (b^2*Pi*x^2)/2],x]","\int C(b x) \sin \left(c+\frac{1}{2} b^2 \pi  x^2\right) \, dx","\frac{1}{8} i b x^2 \cos (c) \, _2F_2\left(1,1;\frac{3}{2},2;-\frac{1}{2} i b^2 \pi  x^2\right)-\frac{1}{8} i b x^2 \cos (c) \, _2F_2\left(1,1;\frac{3}{2},2;\frac{1}{2} i b^2 \pi  x^2\right)+\frac{\cos (c) C(b x) S(b x)}{2 b}+\frac{\sin (c) C(b x)^2}{2 b}",1,"Integrate[FresnelC[b*x]*Sin[c + (b^2*Pi*x^2)/2], x]","F",-1
173,0,0,101,0.0479536,"\int \cos \left(c+\frac{1}{2} b^2 \pi  x^2\right) C(b x) \, dx","Integrate[Cos[c + (b^2*Pi*x^2)/2]*FresnelC[b*x],x]","\int \cos \left(c+\frac{1}{2} b^2 \pi  x^2\right) C(b x) \, dx","-\frac{1}{8} i b x^2 \sin (c) \, _2F_2\left(1,1;\frac{3}{2},2;-\frac{1}{2} i b^2 \pi  x^2\right)+\frac{1}{8} i b x^2 \sin (c) \, _2F_2\left(1,1;\frac{3}{2},2;\frac{1}{2} i b^2 \pi  x^2\right)-\frac{\sin (c) C(b x) S(b x)}{2 b}+\frac{\cos (c) C(b x)^2}{2 b}",1,"Integrate[Cos[c + (b^2*Pi*x^2)/2]*FresnelC[b*x], x]","F",-1
174,1,13,13,0.0102763,"\int \cos \left(\frac{1}{2} b^2 \pi  x^2\right) C(b x)^2 \, dx","Integrate[Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x]^2,x]","\frac{C(b x)^3}{3 b}","\frac{C(b x)^3}{3 b}",1,"FresnelC[b*x]^3/(3*b)","A",1
175,1,13,13,0.0084184,"\int \cos \left(\frac{1}{2} b^2 \pi  x^2\right) C(b x) \, dx","Integrate[Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x],x]","\frac{C(b x)^2}{2 b}","\frac{C(b x)^2}{2 b}",1,"FresnelC[b*x]^2/(2*b)","A",1
176,1,9,9,0.0133719,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right)}{C(b x)} \, dx","Integrate[Cos[(b^2*Pi*x^2)/2]/FresnelC[b*x],x]","\frac{\log (C(b x))}{b}","\frac{\log (C(b x))}{b}",1,"Log[FresnelC[b*x]]/b","A",1
177,1,11,11,0.0092327,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right)}{C(b x)^2} \, dx","Integrate[Cos[(b^2*Pi*x^2)/2]/FresnelC[b*x]^2,x]","-\frac{1}{b C(b x)}","-\frac{1}{b C(b x)}",1,"-(1/(b*FresnelC[b*x]))","A",1
178,1,13,13,0.0088268,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right)}{C(b x)^3} \, dx","Integrate[Cos[(b^2*Pi*x^2)/2]/FresnelC[b*x]^3,x]","-\frac{1}{2 b C(b x)^2}","-\frac{1}{2 b C(b x)^2}",1,"-1/2*1/(b*FresnelC[b*x]^2)","A",1
179,1,17,17,0.0146494,"\int \cos \left(\frac{1}{2} b^2 \pi  x^2\right) C(b x)^n \, dx","Integrate[Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x]^n,x]","\frac{C(b x)^{n+1}}{b (n+1)}","\frac{C(b x)^{n+1}}{b (n+1)}",1,"FresnelC[b*x]^(1 + n)/(b*(1 + n))","A",1
180,1,231,231,0.0144951,"\int x^8 \cos \left(\frac{1}{2} b^2 \pi  x^2\right) C(b x) \, dx","Integrate[x^8*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x],x]","\frac{105 C(b x)^2}{2 \pi ^4 b^9}+\frac{105 x^2}{4 \pi ^4 b^7}-\frac{7 x^6}{12 \pi ^2 b^3}+\frac{x^7 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{40 \sin \left(\pi  b^2 x^2\right)}{\pi ^5 b^9}-\frac{105 x C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^4 b^8}-\frac{55 x^2 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^4 b^7}-\frac{35 x^3 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}-\frac{5 x^4 \sin \left(\pi  b^2 x^2\right)}{2 \pi ^3 b^5}+\frac{7 x^5 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}+\frac{x^6 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}","\frac{105 C(b x)^2}{2 \pi ^4 b^9}+\frac{105 x^2}{4 \pi ^4 b^7}-\frac{7 x^6}{12 \pi ^2 b^3}+\frac{x^7 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{40 \sin \left(\pi  b^2 x^2\right)}{\pi ^5 b^9}-\frac{105 x C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^4 b^8}-\frac{55 x^2 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^4 b^7}-\frac{35 x^3 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}-\frac{5 x^4 \sin \left(\pi  b^2 x^2\right)}{2 \pi ^3 b^5}+\frac{7 x^5 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}+\frac{x^6 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}",1,"(105*x^2)/(4*b^7*Pi^4) - (7*x^6)/(12*b^3*Pi^2) - (55*x^2*Cos[b^2*Pi*x^2])/(4*b^7*Pi^4) + (x^6*Cos[b^2*Pi*x^2])/(4*b^3*Pi^2) - (105*x*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(b^8*Pi^4) + (7*x^5*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(b^4*Pi^2) + (105*FresnelC[b*x]^2)/(2*b^9*Pi^4) - (35*x^3*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^6*Pi^3) + (x^7*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^2*Pi) + (40*Sin[b^2*Pi*x^2])/(b^9*Pi^5) - (5*x^4*Sin[b^2*Pi*x^2])/(2*b^5*Pi^3)","A",1
181,1,154,215,0.2718901,"\int x^7 \cos \left(\frac{1}{2} b^2 \pi  x^2\right) C(b x) \, dx","Integrate[x^7*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x],x]","\frac{160 C(b x) \left(\pi  b^2 x^2 \left(\pi ^2 b^4 x^4-24\right) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)+6 \left(\pi ^2 b^4 x^4-8\right) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)\right)+2 b x \left(5 \left(4 \pi ^2 b^4 x^4-147\right) \cos \left(\pi  b^2 x^2\right)-2 \left(24 \pi ^2 b^4 x^4+85 \pi  b^2 x^2 \sin \left(\pi  b^2 x^2\right)-960\right)\right)+2655 \sqrt{2} C\left(\sqrt{2} b x\right)}{160 \pi ^4 b^8}","\frac{531 C\left(\sqrt{2} b x\right)}{16 \sqrt{2} \pi ^4 b^8}+\frac{24 x}{\pi ^4 b^7}-\frac{3 x^5}{5 \pi ^2 b^3}+\frac{x^6 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{48 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^4 b^8}-\frac{147 x \cos \left(\pi  b^2 x^2\right)}{16 \pi ^4 b^7}-\frac{24 x^2 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}-\frac{17 x^3 \sin \left(\pi  b^2 x^2\right)}{8 \pi ^3 b^5}+\frac{6 x^4 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}+\frac{x^5 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}",1,"(2655*Sqrt[2]*FresnelC[Sqrt[2]*b*x] + 160*FresnelC[b*x]*(6*(-8 + b^4*Pi^2*x^4)*Cos[(b^2*Pi*x^2)/2] + b^2*Pi*x^2*(-24 + b^4*Pi^2*x^4)*Sin[(b^2*Pi*x^2)/2]) + 2*b*x*(5*(-147 + 4*b^4*Pi^2*x^4)*Cos[b^2*Pi*x^2] - 2*(-960 + 24*b^4*Pi^2*x^4 + 85*b^2*Pi*x^2*Sin[b^2*Pi*x^2])))/(160*b^8*Pi^4)","A",1
182,0,0,247,0.4424365,"\int x^6 \cos \left(\frac{1}{2} b^2 \pi  x^2\right) C(b x) \, dx","Integrate[x^6*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x],x]","\int x^6 \cos \left(\frac{1}{2} b^2 \pi  x^2\right) C(b x) \, dx","\frac{15 i x^2 \, _2F_2\left(1,1;\frac{3}{2},2;-\frac{1}{2} i b^2 \pi  x^2\right)}{8 \pi ^3 b^5}-\frac{15 i x^2 \, _2F_2\left(1,1;\frac{3}{2},2;\frac{1}{2} i b^2 \pi  x^2\right)}{8 \pi ^3 b^5}+\frac{15 C(b x) S(b x)}{2 \pi ^3 b^7}-\frac{5 x^4}{8 \pi ^2 b^3}+\frac{x^5 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{11 \cos \left(\pi  b^2 x^2\right)}{2 \pi ^4 b^7}-\frac{15 x C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}-\frac{7 x^2 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^3 b^5}+\frac{5 x^3 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}+\frac{x^4 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}",1,"Integrate[x^6*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x], x]","F",-1
183,1,120,157,0.1403155,"\int x^5 \cos \left(\frac{1}{2} b^2 \pi  x^2\right) C(b x) \, dx","Integrate[x^5*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x],x]","\frac{-32 \pi  b^3 x^3-66 b x \sin \left(\pi  b^2 x^2\right)+48 C(b x) \left(4 \pi  b^2 x^2 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)+\left(\pi ^2 b^4 x^4-8\right) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)\right)+12 \pi  b^3 x^3 \cos \left(\pi  b^2 x^2\right)+129 \sqrt{2} S\left(\sqrt{2} b x\right)}{48 \pi ^3 b^6}","\frac{43 S\left(\sqrt{2} b x\right)}{8 \sqrt{2} \pi ^3 b^6}-\frac{2 x^3}{3 \pi ^2 b^3}+\frac{x^4 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{8 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}-\frac{11 x \sin \left(\pi  b^2 x^2\right)}{8 \pi ^3 b^5}+\frac{4 x^2 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}+\frac{x^3 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}",1,"(-32*b^3*Pi*x^3 + 12*b^3*Pi*x^3*Cos[b^2*Pi*x^2] + 129*Sqrt[2]*FresnelS[Sqrt[2]*b*x] + 48*FresnelC[b*x]*(4*b^2*Pi*x^2*Cos[(b^2*Pi*x^2)/2] + (-8 + b^4*Pi^2*x^4)*Sin[(b^2*Pi*x^2)/2]) - 66*b*x*Sin[b^2*Pi*x^2])/(48*b^6*Pi^3)","A",1
184,1,120,120,0.01225,"\int x^4 \cos \left(\frac{1}{2} b^2 \pi  x^2\right) C(b x) \, dx","Integrate[x^4*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x],x]","-\frac{3 C(b x)^2}{2 \pi ^2 b^5}-\frac{3 x^2}{4 \pi ^2 b^3}+\frac{x^3 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{\sin \left(\pi  b^2 x^2\right)}{\pi ^3 b^5}+\frac{3 x C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}+\frac{x^2 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}","-\frac{3 C(b x)^2}{2 \pi ^2 b^5}-\frac{3 x^2}{4 \pi ^2 b^3}+\frac{x^3 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{\sin \left(\pi  b^2 x^2\right)}{\pi ^3 b^5}+\frac{3 x C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}+\frac{x^2 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}",1,"(-3*x^2)/(4*b^3*Pi^2) + (x^2*Cos[b^2*Pi*x^2])/(4*b^3*Pi^2) + (3*x*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(b^4*Pi^2) - (3*FresnelC[b*x]^2)/(2*b^5*Pi^2) + (x^3*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^2*Pi) - Sin[b^2*Pi*x^2]/(b^5*Pi^3)","A",1
185,1,83,104,0.0954658,"\int x^3 \cos \left(\frac{1}{2} b^2 \pi  x^2\right) C(b x) \, dx","Integrate[x^3*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x],x]","\frac{8 C(b x) \left(\pi  b^2 x^2 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)+2 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)\right)+2 b x \left(\cos \left(\pi  b^2 x^2\right)-4\right)-5 \sqrt{2} C\left(\sqrt{2} b x\right)}{8 \pi ^2 b^4}","-\frac{5 C\left(\sqrt{2} b x\right)}{4 \sqrt{2} \pi ^2 b^4}-\frac{x}{\pi ^2 b^3}+\frac{x^2 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{2 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}+\frac{x \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}",1,"(2*b*x*(-4 + Cos[b^2*Pi*x^2]) - 5*Sqrt[2]*FresnelC[Sqrt[2]*b*x] + 8*FresnelC[b*x]*(2*Cos[(b^2*Pi*x^2)/2] + b^2*Pi*x^2*Sin[(b^2*Pi*x^2)/2]))/(8*b^4*Pi^2)","A",1
186,0,0,136,0.2388449,"\int x^2 \cos \left(\frac{1}{2} b^2 \pi  x^2\right) C(b x) \, dx","Integrate[x^2*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x],x]","\int x^2 \cos \left(\frac{1}{2} b^2 \pi  x^2\right) C(b x) \, dx","-\frac{i x^2 \, _2F_2\left(1,1;\frac{3}{2},2;-\frac{1}{2} i b^2 \pi  x^2\right)}{8 \pi  b}+\frac{i x^2 \, _2F_2\left(1,1;\frac{3}{2},2;\frac{1}{2} i b^2 \pi  x^2\right)}{8 \pi  b}-\frac{C(b x) S(b x)}{2 \pi  b^3}+\frac{x C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{\cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}",1,"Integrate[x^2*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x], x]","F",-1
187,1,44,48,0.0308342,"\int x \cos \left(\frac{1}{2} b^2 \pi  x^2\right) C(b x) \, dx","Integrate[x*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x],x]","-\frac{\sqrt{2} S\left(\sqrt{2} b x\right)-4 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi  b^2}","\frac{C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{S\left(\sqrt{2} b x\right)}{2 \sqrt{2} \pi  b^2}",1,"-1/4*(Sqrt[2]*FresnelS[Sqrt[2]*b*x] - 4*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^2*Pi)","A",1
188,1,13,13,0.0025275,"\int \cos \left(\frac{1}{2} b^2 \pi  x^2\right) C(b x) \, dx","Integrate[Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x],x]","\frac{C(b x)^2}{2 b}","\frac{C(b x)^2}{2 b}",1,"FresnelC[b*x]^2/(2*b)","A",1
189,0,0,23,0.0347591,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) C(b x)}{x} \, dx","Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/x,x]","\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) C(b x)}{x} \, dx","\text{Int}\left(\frac{C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)",0,"Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/x, x]","A",-1
190,0,0,23,0.0372536,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) C(b x)}{x^2} \, dx","Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/x^2,x]","\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) C(b x)}{x^2} \, dx","\text{Int}\left(\frac{C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x^2},x\right)",0,"Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/x^2, x]","A",-1
191,0,0,102,0.0319063,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) C(b x)}{x^3} \, dx","Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/x^3,x]","\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) C(b x)}{x^3} \, dx","-\frac{1}{2} \pi  b^2 \text{Int}\left(\frac{C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)-\frac{C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{2 x^2}-\frac{\pi  b^2 S\left(\sqrt{2} b x\right)}{2 \sqrt{2}}-\frac{b \cos \left(\pi  b^2 x^2\right)}{4 x}-\frac{b}{4 x}",0,"Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/x^3, x]","A",-1
192,1,109,109,0.0101337,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) C(b x)}{x^4} \, dx","Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/x^4,x]","-\frac{1}{6} \pi ^2 b^3 C(b x)^2+\frac{\pi  b^2 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 x}-\frac{C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 x^3}-\frac{b \cos \left(\pi  b^2 x^2\right)}{12 x^2}-\frac{1}{6} \pi  b^3 \text{Si}\left(b^2 \pi  x^2\right)-\frac{b}{12 x^2}","-\frac{1}{6} \pi ^2 b^3 C(b x)^2+\frac{\pi  b^2 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 x}-\frac{C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 x^3}-\frac{b \cos \left(\pi  b^2 x^2\right)}{12 x^2}-\frac{1}{6} \pi  b^3 \text{Si}\left(b^2 \pi  x^2\right)-\frac{b}{12 x^2}",1,"-1/12*b/x^2 - (b*Cos[b^2*Pi*x^2])/(12*x^2) - (Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(3*x^3) - (b^3*Pi^2*FresnelC[b*x]^2)/6 + (b^2*Pi*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(3*x) - (b^3*Pi*SinIntegral[b^2*Pi*x^2])/6","A",1
193,0,0,153,0.0419015,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) C(b x)}{x^5} \, dx","Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/x^5,x]","\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) C(b x)}{x^5} \, dx","-\frac{1}{8} \pi ^2 b^4 \text{Int}\left(\frac{C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)-\frac{7 \pi ^2 b^4 C\left(\sqrt{2} b x\right)}{24 \sqrt{2}}+\frac{\pi  b^2 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{8 x^2}-\frac{C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 x^4}-\frac{b \cos \left(\pi  b^2 x^2\right)}{24 x^3}+\frac{7 \pi  b^3 \sin \left(\pi  b^2 x^2\right)}{48 x}-\frac{b}{24 x^3}",0,"Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/x^5, x]","A",-1
194,0,0,148,0.0522634,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) C(b x)}{x^6} \, dx","Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/x^6,x]","\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) C(b x)}{x^6} \, dx","-\frac{1}{15} \pi ^2 b^4 \text{Int}\left(\frac{C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x^2},x\right)-\frac{C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 x^5}+\frac{\pi  b^2 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{15 x^3}-\frac{b \cos \left(\pi  b^2 x^2\right)}{40 x^4}-\frac{1}{24} \pi ^2 b^5 \text{Ci}\left(b^2 \pi  x^2\right)+\frac{\pi  b^3 \sin \left(\pi  b^2 x^2\right)}{24 x^2}-\frac{b}{40 x^4}",0,"Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/x^6, x]","A",-1
195,0,0,241,0.0295237,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) C(b x)}{x^7} \, dx","Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/x^7,x]","\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) C(b x)}{x^7} \, dx","\frac{1}{48} \pi ^3 b^6 \text{Int}\left(\frac{C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)+\frac{1}{45} \sqrt{2} \pi ^3 b^6 S\left(\sqrt{2} b x\right)+\frac{7 \pi ^3 b^6 S\left(\sqrt{2} b x\right)}{144 \sqrt{2}}+\frac{\pi ^2 b^5}{96 x}-\frac{C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 x^6}+\frac{\pi  b^2 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{24 x^4}-\frac{b \cos \left(\pi  b^2 x^2\right)}{60 x^5}+\frac{67 \pi ^2 b^5 \cos \left(\pi  b^2 x^2\right)}{1440 x}+\frac{\pi ^2 b^4 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{48 x^2}+\frac{13 \pi  b^3 \sin \left(\pi  b^2 x^2\right)}{720 x^3}-\frac{b}{60 x^5}",0,"Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/x^7, x]","A",-1
196,1,224,224,0.0146852,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) C(b x)}{x^8} \, dx","Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/x^8,x]","\frac{1}{210} \pi ^4 b^7 C(b x)^2+\frac{\pi ^2 b^5}{420 x^2}-\frac{C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 x^7}+\frac{\pi  b^2 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{35 x^5}-\frac{b \cos \left(\pi  b^2 x^2\right)}{84 x^6}+\frac{1}{70} \pi ^3 b^7 \text{Si}\left(b^2 \pi  x^2\right)-\frac{\pi ^3 b^6 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{105 x}+\frac{\pi ^2 b^5 \cos \left(\pi  b^2 x^2\right)}{84 x^2}+\frac{\pi ^2 b^4 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{105 x^3}+\frac{\pi  b^3 \sin \left(\pi  b^2 x^2\right)}{105 x^4}-\frac{b}{84 x^6}","\frac{1}{210} \pi ^4 b^7 C(b x)^2+\frac{\pi ^2 b^5}{420 x^2}-\frac{C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 x^7}+\frac{\pi  b^2 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{35 x^5}-\frac{b \cos \left(\pi  b^2 x^2\right)}{84 x^6}+\frac{1}{70} \pi ^3 b^7 \text{Si}\left(b^2 \pi  x^2\right)-\frac{\pi ^3 b^6 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{105 x}+\frac{\pi ^2 b^5 \cos \left(\pi  b^2 x^2\right)}{84 x^2}+\frac{\pi ^2 b^4 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{105 x^3}+\frac{\pi  b^3 \sin \left(\pi  b^2 x^2\right)}{105 x^4}-\frac{b}{84 x^6}",1,"-1/84*b/x^6 + (b^5*Pi^2)/(420*x^2) - (b*Cos[b^2*Pi*x^2])/(84*x^6) + (b^5*Pi^2*Cos[b^2*Pi*x^2])/(84*x^2) - (Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(7*x^7) + (b^4*Pi^2*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(105*x^3) + (b^7*Pi^4*FresnelC[b*x]^2)/210 + (b^2*Pi*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(35*x^5) - (b^6*Pi^3*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(105*x) + (b^3*Pi*Sin[b^2*Pi*x^2])/(105*x^4) + (b^7*Pi^3*SinIntegral[b^2*Pi*x^2])/70","A",1
197,0,0,268,0.041114,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) C(b x)}{x^9} \, dx","Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/x^9,x]","\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) C(b x)}{x^9} \, dx","\frac{1}{384} \pi ^4 b^8 \text{Int}\left(\frac{C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)+\frac{853 \pi ^4 b^8 C\left(\sqrt{2} b x\right)}{40320 \sqrt{2}}+\frac{\pi ^2 b^5}{1152 x^3}-\frac{C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{8 x^8}+\frac{\pi  b^2 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{48 x^6}-\frac{b \cos \left(\pi  b^2 x^2\right)}{112 x^7}-\frac{853 \pi ^3 b^7 \sin \left(\pi  b^2 x^2\right)}{80640 x}-\frac{\pi ^3 b^6 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{384 x^2}+\frac{187 \pi ^2 b^5 \cos \left(\pi  b^2 x^2\right)}{40320 x^3}+\frac{\pi ^2 b^4 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{192 x^4}+\frac{19 \pi  b^3 \sin \left(\pi  b^2 x^2\right)}{3360 x^5}-\frac{b}{112 x^7}",0,"Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/x^9, x]","A",-1
198,0,0,263,0.0454883,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) C(b x)}{x^{10}} \, dx","Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/x^10,x]","\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) C(b x)}{x^{10}} \, dx","\frac{1}{945} \pi ^4 b^8 \text{Int}\left(\frac{C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x^2},x\right)+\frac{\pi ^2 b^5}{2520 x^4}-\frac{C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{9 x^9}+\frac{\pi  b^2 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{63 x^7}-\frac{b \cos \left(\pi  b^2 x^2\right)}{144 x^8}+\frac{5 \pi ^4 b^9 \text{Ci}\left(b^2 \pi  x^2\right)}{2016}-\frac{5 \pi ^3 b^7 \sin \left(\pi  b^2 x^2\right)}{2016 x^2}-\frac{\pi ^3 b^6 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{945 x^3}+\frac{67 \pi ^2 b^5 \cos \left(\pi  b^2 x^2\right)}{30240 x^4}+\frac{\pi ^2 b^4 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{315 x^5}+\frac{11 \pi  b^3 \sin \left(\pi  b^2 x^2\right)}{3024 x^6}-\frac{b}{144 x^8}",0,"Integrate[(Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/x^10, x]","A",-1
199,0,0,22,0.080662,"\int C(b x)^n \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Integrate[FresnelC[b*x]^n*Sin[(b^2*Pi*x^2)/2],x]","\int C(b x)^n \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","\text{Int}\left(\sin \left(\frac{1}{2} \pi  b^2 x^2\right) C(b x)^n,x\right)",0,"Integrate[FresnelC[b*x]^n*Sin[(b^2*Pi*x^2)/2], x]","A",-1
200,0,0,308,0.0530973,"\int x^8 C(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Integrate[x^8*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2],x]","\int x^8 C(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","\frac{105 i x^2 \, _2F_2\left(1,1;\frac{3}{2},2;-\frac{1}{2} i b^2 \pi  x^2\right)}{8 \pi ^4 b^7}-\frac{105 i x^2 \, _2F_2\left(1,1;\frac{3}{2},2;\frac{1}{2} i b^2 \pi  x^2\right)}{8 \pi ^4 b^7}+\frac{105 C(b x) S(b x)}{2 \pi ^4 b^9}-\frac{35 x^4}{8 \pi ^3 b^5}-\frac{x^7 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{40 \cos \left(\pi  b^2 x^2\right)}{\pi ^5 b^9}-\frac{105 x C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^4 b^8}-\frac{55 x^2 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^4 b^7}+\frac{35 x^3 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}+\frac{5 x^4 \cos \left(\pi  b^2 x^2\right)}{2 \pi ^3 b^5}+\frac{7 x^5 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}+\frac{x^6 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}+\frac{x^8}{16 \pi  b}",1,"Integrate[x^8*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2], x]","F",-1
201,1,163,218,0.1806425,"\int x^7 C(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Integrate[x^7*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2],x]","\frac{16 \pi ^3 b^7 x^7-896 \pi  b^3 x^3-2058 b x \sin \left(\pi  b^2 x^2\right)+56 \pi ^2 b^5 x^5 \sin \left(\pi  b^2 x^2\right)-224 C(b x) \left(\pi  b^2 x^2 \left(\pi ^2 b^4 x^4-24\right) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)-6 \left(\pi ^2 b^4 x^4-8\right) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)\right)+476 \pi  b^3 x^3 \cos \left(\pi  b^2 x^2\right)+3717 \sqrt{2} S\left(\sqrt{2} b x\right)}{224 \pi ^4 b^8}","\frac{531 S\left(\sqrt{2} b x\right)}{16 \sqrt{2} \pi ^4 b^8}-\frac{4 x^3}{\pi ^3 b^5}-\frac{x^6 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{48 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^4 b^8}-\frac{147 x \sin \left(\pi  b^2 x^2\right)}{16 \pi ^4 b^7}+\frac{24 x^2 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}+\frac{17 x^3 \cos \left(\pi  b^2 x^2\right)}{8 \pi ^3 b^5}+\frac{6 x^4 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}+\frac{x^5 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}+\frac{x^7}{14 \pi  b}",1,"(-896*b^3*Pi*x^3 + 16*b^7*Pi^3*x^7 + 476*b^3*Pi*x^3*Cos[b^2*Pi*x^2] + 3717*Sqrt[2]*FresnelS[Sqrt[2]*b*x] - 224*FresnelC[b*x]*(b^2*Pi*x^2*(-24 + b^4*Pi^2*x^4)*Cos[(b^2*Pi*x^2)/2] - 6*(-8 + b^4*Pi^2*x^4)*Sin[(b^2*Pi*x^2)/2]) - 2058*b*x*Sin[b^2*Pi*x^2] + 56*b^5*Pi^2*x^5*Sin[b^2*Pi*x^2])/(224*b^8*Pi^4)","A",1
202,1,185,185,0.0117816,"\int x^6 C(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Integrate[x^6*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2],x]","-\frac{15 C(b x)^2}{2 \pi ^3 b^7}-\frac{15 x^2}{4 \pi ^3 b^5}-\frac{x^5 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{11 \sin \left(\pi  b^2 x^2\right)}{2 \pi ^4 b^7}+\frac{15 x C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}+\frac{7 x^2 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^3 b^5}+\frac{5 x^3 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}+\frac{x^4 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}+\frac{x^6}{12 \pi  b}","-\frac{15 C(b x)^2}{2 \pi ^3 b^7}-\frac{15 x^2}{4 \pi ^3 b^5}-\frac{x^5 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{11 \sin \left(\pi  b^2 x^2\right)}{2 \pi ^4 b^7}+\frac{15 x C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}+\frac{7 x^2 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^3 b^5}+\frac{5 x^3 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}+\frac{x^4 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}+\frac{x^6}{12 \pi  b}",1,"(-15*x^2)/(4*b^5*Pi^3) + x^6/(12*b*Pi) + (7*x^2*Cos[b^2*Pi*x^2])/(4*b^5*Pi^3) + (15*x*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(b^6*Pi^3) - (x^5*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(b^2*Pi) - (15*FresnelC[b*x]^2)/(2*b^7*Pi^3) + (5*x^3*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^4*Pi^2) - (11*Sin[b^2*Pi*x^2])/(2*b^7*Pi^4) + (x^4*Sin[b^2*Pi*x^2])/(4*b^3*Pi^2)","A",1
203,1,126,167,0.194662,"\int x^5 C(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Integrate[x^5*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2],x]","\frac{-80 C(b x) \left(\left(\pi ^2 b^4 x^4-8\right) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)-4 \pi  b^2 x^2 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)\right)+2 b x \left(4 \pi ^2 b^4 x^4+10 \pi  b^2 x^2 \sin \left(\pi  b^2 x^2\right)+55 \cos \left(\pi  b^2 x^2\right)-160\right)-215 \sqrt{2} C\left(\sqrt{2} b x\right)}{80 \pi ^3 b^6}","-\frac{43 C\left(\sqrt{2} b x\right)}{8 \sqrt{2} \pi ^3 b^6}-\frac{4 x}{\pi ^3 b^5}-\frac{x^4 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{8 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}+\frac{11 x \cos \left(\pi  b^2 x^2\right)}{8 \pi ^3 b^5}+\frac{4 x^2 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}+\frac{x^3 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}+\frac{x^5}{10 \pi  b}",1,"(-215*Sqrt[2]*FresnelC[Sqrt[2]*b*x] - 80*FresnelC[b*x]*((-8 + b^4*Pi^2*x^4)*Cos[(b^2*Pi*x^2)/2] - 4*b^2*Pi*x^2*Sin[(b^2*Pi*x^2)/2]) + 2*b*x*(-160 + 4*b^4*Pi^2*x^4 + 55*Cos[b^2*Pi*x^2] + 10*b^2*Pi*x^2*Sin[b^2*Pi*x^2]))/(80*b^6*Pi^3)","A",1
204,0,0,196,0.046452,"\int x^4 C(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Integrate[x^4*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2],x]","\int x^4 C(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","-\frac{3 i x^2 \, _2F_2\left(1,1;\frac{3}{2},2;-\frac{1}{2} i b^2 \pi  x^2\right)}{8 \pi ^2 b^3}+\frac{3 i x^2 \, _2F_2\left(1,1;\frac{3}{2},2;\frac{1}{2} i b^2 \pi  x^2\right)}{8 \pi ^2 b^3}-\frac{3 C(b x) S(b x)}{2 \pi ^2 b^5}-\frac{x^3 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{\cos \left(\pi  b^2 x^2\right)}{\pi ^3 b^5}+\frac{3 x C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}+\frac{x^2 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}+\frac{x^4}{8 \pi  b}",1,"Integrate[x^4*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2], x]","F",-1
205,1,90,109,0.0957525,"\int x^3 C(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Integrate[x^3*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2],x]","\frac{4 \pi  b^3 x^3-24 C(b x) \left(\pi  b^2 x^2 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)-2 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)\right)+6 b x \sin \left(\pi  b^2 x^2\right)-15 \sqrt{2} S\left(\sqrt{2} b x\right)}{24 \pi ^2 b^4}","-\frac{5 S\left(\sqrt{2} b x\right)}{4 \sqrt{2} \pi ^2 b^4}-\frac{x^2 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{2 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}+\frac{x \sin \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}+\frac{x^3}{6 \pi  b}",1,"(4*b^3*Pi*x^3 - 15*Sqrt[2]*FresnelS[Sqrt[2]*b*x] - 24*FresnelC[b*x]*(b^2*Pi*x^2*Cos[(b^2*Pi*x^2)/2] - 2*Sin[(b^2*Pi*x^2)/2]) + 6*b*x*Sin[b^2*Pi*x^2])/(24*b^4*Pi^2)","A",1
206,1,74,74,0.0047057,"\int x^2 C(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Integrate[x^2*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2],x]","\frac{C(b x)^2}{2 \pi  b^3}-\frac{x C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{\sin \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}+\frac{x^2}{4 \pi  b}","\frac{C(b x)^2}{2 \pi  b^3}-\frac{x C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{\sin \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}+\frac{x^2}{4 \pi  b}",1,"x^2/(4*b*Pi) - (x*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(b^2*Pi) + FresnelC[b*x]^2/(2*b^3*Pi) + Sin[b^2*Pi*x^2]/(4*b^3*Pi^2)","A",1
207,1,48,60,0.0261193,"\int x C(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Integrate[x*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2],x]","\frac{-4 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)+\sqrt{2} C\left(\sqrt{2} b x\right)+2 b x}{4 \pi  b^2}","-\frac{C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{C\left(\sqrt{2} b x\right)}{2 \sqrt{2} \pi  b^2}+\frac{x}{2 \pi  b}",1,"(2*b*x - 4*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x] + Sqrt[2]*FresnelC[Sqrt[2]*b*x])/(4*b^2*Pi)","A",1
208,0,0,80,0.0173065,"\int C(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Integrate[FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2],x]","\int C(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","\frac{1}{8} i b x^2 \, _2F_2\left(1,1;\frac{3}{2},2;-\frac{1}{2} i b^2 \pi  x^2\right)-\frac{1}{8} i b x^2 \, _2F_2\left(1,1;\frac{3}{2},2;\frac{1}{2} i b^2 \pi  x^2\right)+\frac{C(b x) S(b x)}{2 b}",1,"Integrate[FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2], x]","F",-1
209,0,0,23,0.0371741,"\int \frac{C(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x} \, dx","Integrate[(FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/x,x]","\int \frac{C(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x} \, dx","\text{Int}\left(\frac{C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)",0,"Integrate[(FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/x, x]","A",-1
210,1,48,48,0.0078608,"\int \frac{C(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^2} \, dx","Integrate[(FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/x^2,x]","-\frac{C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x}+\frac{1}{4} b \text{Si}\left(b^2 \pi  x^2\right)+\frac{1}{2} \pi  b C(b x)^2","-\frac{C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x}+\frac{1}{4} b \text{Si}\left(b^2 \pi  x^2\right)+\frac{1}{2} \pi  b C(b x)^2",1,"(b*Pi*FresnelC[b*x]^2)/2 - (FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/x + (b*SinIntegral[b^2*Pi*x^2])/4","A",1
211,0,0,94,0.045451,"\int \frac{C(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^3} \, dx","Integrate[(FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/x^3,x]","\int \frac{C(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^3} \, dx","\frac{1}{2} \pi  b^2 \text{Int}\left(\frac{C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)-\frac{C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{2 x^2}+\frac{\pi  b^2 C\left(\sqrt{2} b x\right)}{2 \sqrt{2}}-\frac{b \sin \left(\pi  b^2 x^2\right)}{4 x}",0,"Integrate[(FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/x^3, x]","A",-1
212,0,0,89,0.0388271,"\int \frac{C(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^4} \, dx","Integrate[(FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/x^4,x]","\int \frac{C(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^4} \, dx","\frac{1}{3} \pi  b^2 \text{Int}\left(\frac{C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x^2},x\right)-\frac{C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 x^3}-\frac{b \sin \left(\pi  b^2 x^2\right)}{12 x^2}+\frac{1}{12} \pi  b^3 \text{Ci}\left(b^2 \pi  x^2\right)",0,"Integrate[(FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/x^4, x]","A",-1
213,0,0,156,0.0409601,"\int \frac{C(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^5} \, dx","Integrate[(FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/x^5,x]","\int \frac{C(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^5} \, dx","-\frac{1}{8} \pi ^2 b^4 \text{Int}\left(\frac{C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)-\frac{7 \pi ^2 b^4 S\left(\sqrt{2} b x\right)}{24 \sqrt{2}}-\frac{\pi  b^3}{16 x}-\frac{\pi  b^2 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{8 x^2}-\frac{C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 x^4}-\frac{b \sin \left(\pi  b^2 x^2\right)}{24 x^3}-\frac{7 \pi  b^3 \cos \left(\pi  b^2 x^2\right)}{48 x}",0,"Integrate[(FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/x^5, x]","A",-1
214,1,163,163,0.0117703,"\int \frac{C(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^6} \, dx","Integrate[(FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/x^6,x]","-\frac{1}{30} \pi ^3 b^5 C(b x)^2-\frac{\pi  b^3}{60 x^2}-\frac{C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 x^5}-\frac{\pi  b^2 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{15 x^3}-\frac{b \sin \left(\pi  b^2 x^2\right)}{40 x^4}-\frac{7}{120} \pi ^2 b^5 \text{Si}\left(b^2 \pi  x^2\right)+\frac{\pi ^2 b^4 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{15 x}-\frac{\pi  b^3 \cos \left(\pi  b^2 x^2\right)}{24 x^2}","-\frac{1}{30} \pi ^3 b^5 C(b x)^2-\frac{\pi  b^3}{60 x^2}-\frac{C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 x^5}-\frac{\pi  b^2 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{15 x^3}-\frac{b \sin \left(\pi  b^2 x^2\right)}{40 x^4}-\frac{7}{120} \pi ^2 b^5 \text{Si}\left(b^2 \pi  x^2\right)+\frac{\pi ^2 b^4 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{15 x}-\frac{\pi  b^3 \cos \left(\pi  b^2 x^2\right)}{24 x^2}",1,"-1/60*(b^3*Pi)/x^2 - (b^3*Pi*Cos[b^2*Pi*x^2])/(24*x^2) - (b^2*Pi*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(15*x^3) - (b^5*Pi^3*FresnelC[b*x]^2)/30 - (FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(5*x^5) + (b^4*Pi^2*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(15*x) - (b*Sin[b^2*Pi*x^2])/(40*x^4) - (7*b^5*Pi^2*SinIntegral[b^2*Pi*x^2])/120","A",1
215,0,0,231,0.0374533,"\int \frac{C(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^7} \, dx","Integrate[(FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/x^7,x]","\int \frac{C(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^7} \, dx","-\frac{1}{48} \pi ^3 b^6 \text{Int}\left(\frac{C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)-\frac{1}{45} \sqrt{2} \pi ^3 b^6 C\left(\sqrt{2} b x\right)-\frac{7 \pi ^3 b^6 C\left(\sqrt{2} b x\right)}{144 \sqrt{2}}-\frac{\pi  b^3}{144 x^3}-\frac{C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 x^6}-\frac{\pi  b^2 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{24 x^4}-\frac{b \sin \left(\pi  b^2 x^2\right)}{60 x^5}+\frac{67 \pi ^2 b^5 \sin \left(\pi  b^2 x^2\right)}{1440 x}+\frac{\pi ^2 b^4 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{48 x^2}-\frac{13 \pi  b^3 \cos \left(\pi  b^2 x^2\right)}{720 x^3}",0,"Integrate[(FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/x^7, x]","A",-1
216,0,0,202,0.0333172,"\int \frac{C(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^8} \, dx","Integrate[(FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/x^8,x]","\int \frac{C(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^8} \, dx","-\frac{1}{105} \pi ^3 b^6 \text{Int}\left(\frac{C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x^2},x\right)-\frac{\pi  b^3}{280 x^4}-\frac{C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 x^7}-\frac{\pi  b^2 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{35 x^5}-\frac{b \sin \left(\pi  b^2 x^2\right)}{84 x^6}-\frac{1}{84} \pi ^3 b^7 \text{Ci}\left(b^2 \pi  x^2\right)+\frac{\pi ^2 b^5 \sin \left(\pi  b^2 x^2\right)}{84 x^2}+\frac{\pi ^2 b^4 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{105 x^3}-\frac{\pi  b^3 \cos \left(\pi  b^2 x^2\right)}{105 x^4}",0,"Integrate[(FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/x^8, x]","A",-1
217,0,0,271,0.043778,"\int \frac{C(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^9} \, dx","Integrate[(FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/x^9,x]","\int \frac{C(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^9} \, dx","\frac{1}{384} \pi ^4 b^8 \text{Int}\left(\frac{C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)+\frac{853 \pi ^4 b^8 S\left(\sqrt{2} b x\right)}{40320 \sqrt{2}}+\frac{\pi ^3 b^7}{768 x}-\frac{\pi  b^3}{480 x^5}-\frac{C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{8 x^8}-\frac{\pi  b^2 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{48 x^6}-\frac{b \sin \left(\pi  b^2 x^2\right)}{112 x^7}+\frac{853 \pi ^3 b^7 \cos \left(\pi  b^2 x^2\right)}{80640 x}+\frac{\pi ^3 b^6 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{384 x^2}+\frac{187 \pi ^2 b^5 \sin \left(\pi  b^2 x^2\right)}{40320 x^3}+\frac{\pi ^2 b^4 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{192 x^4}-\frac{19 \pi  b^3 \cos \left(\pi  b^2 x^2\right)}{3360 x^5}",0,"Integrate[(FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/x^9, x]","A",-1
218,1,278,278,0.0266712,"\int \frac{C(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^{10}} \, dx","Integrate[(FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/x^10,x]","\frac{\pi ^5 b^9 C(b x)^2}{1890}+\frac{\pi ^3 b^7}{3780 x^2}-\frac{\pi  b^3}{756 x^6}-\frac{C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{9 x^9}-\frac{\pi  b^2 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{63 x^7}-\frac{b \sin \left(\pi  b^2 x^2\right)}{144 x^8}+\frac{83 \pi ^4 b^9 \text{Si}\left(b^2 \pi  x^2\right)}{30240}-\frac{\pi ^4 b^8 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{945 x}+\frac{5 \pi ^3 b^7 \cos \left(\pi  b^2 x^2\right)}{2016 x^2}+\frac{\pi ^3 b^6 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{945 x^3}+\frac{67 \pi ^2 b^5 \sin \left(\pi  b^2 x^2\right)}{30240 x^4}+\frac{\pi ^2 b^4 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{315 x^5}-\frac{11 \pi  b^3 \cos \left(\pi  b^2 x^2\right)}{3024 x^6}","\frac{\pi ^5 b^9 C(b x)^2}{1890}+\frac{\pi ^3 b^7}{3780 x^2}-\frac{\pi  b^3}{756 x^6}-\frac{C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{9 x^9}-\frac{\pi  b^2 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{63 x^7}-\frac{b \sin \left(\pi  b^2 x^2\right)}{144 x^8}+\frac{83 \pi ^4 b^9 \text{Si}\left(b^2 \pi  x^2\right)}{30240}-\frac{\pi ^4 b^8 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{945 x}+\frac{5 \pi ^3 b^7 \cos \left(\pi  b^2 x^2\right)}{2016 x^2}+\frac{\pi ^3 b^6 C(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{945 x^3}+\frac{67 \pi ^2 b^5 \sin \left(\pi  b^2 x^2\right)}{30240 x^4}+\frac{\pi ^2 b^4 C(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{315 x^5}-\frac{11 \pi  b^3 \cos \left(\pi  b^2 x^2\right)}{3024 x^6}",1,"-1/756*(b^3*Pi)/x^6 + (b^7*Pi^3)/(3780*x^2) - (11*b^3*Pi*Cos[b^2*Pi*x^2])/(3024*x^6) + (5*b^7*Pi^3*Cos[b^2*Pi*x^2])/(2016*x^2) - (b^2*Pi*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(63*x^7) + (b^6*Pi^3*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(945*x^3) + (b^9*Pi^5*FresnelC[b*x]^2)/1890 - (FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(9*x^9) + (b^4*Pi^2*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(315*x^5) - (b^8*Pi^4*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(945*x) - (b*Sin[b^2*Pi*x^2])/(144*x^8) + (67*b^5*Pi^2*Sin[b^2*Pi*x^2])/(30240*x^4) + (83*b^9*Pi^4*SinIntegral[b^2*Pi*x^2])/30240","A",1