1,1,124,0,0.0883233,"\int x^7 S(b x) \, dx","Int[x^7*FresnelS[b*x],x]","-\frac{105 S(b x)}{8 \pi ^4 b^8}-\frac{7 x^5 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{8 \pi ^2 b^3}+\frac{105 x \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{8 \pi ^4 b^7}+\frac{x^7 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{8 \pi  b}-\frac{35 x^3 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{8 \pi ^3 b^5}+\frac{1}{8} x^8 S(b x)","-\frac{105 S(b x)}{8 \pi ^4 b^8}-\frac{7 x^5 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{8 \pi ^2 b^3}+\frac{105 x \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{8 \pi ^4 b^7}+\frac{x^7 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{8 \pi  b}-\frac{35 x^3 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{8 \pi ^3 b^5}+\frac{1}{8} x^8 S(b x)",1,"(-35*x^3*Cos[(b^2*Pi*x^2)/2])/(8*b^5*Pi^3) + (x^7*Cos[(b^2*Pi*x^2)/2])/(8*b*Pi) - (105*FresnelS[b*x])/(8*b^8*Pi^4) + (x^8*FresnelS[b*x])/8 + (105*x*Sin[(b^2*Pi*x^2)/2])/(8*b^7*Pi^4) - (7*x^5*Sin[(b^2*Pi*x^2)/2])/(8*b^3*Pi^2)","A",6,4,8,0.5000,1,"{6426, 3385, 3386, 3351}"
2,1,109,0,0.1106928,"\int x^6 S(b x) \, dx","Int[x^6*FresnelS[b*x],x]","-\frac{6 x^4 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi ^2 b^3}+\frac{48 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi ^4 b^7}+\frac{x^6 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi  b}-\frac{24 x^2 \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{6 x^4 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi ^2 b^3}+\frac{48 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi ^4 b^7}+\frac{x^6 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi  b}-\frac{24 x^2 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi ^3 b^5}+\frac{1}{7} x^7 S(b x)",1,"(-24*x^2*Cos[(b^2*Pi*x^2)/2])/(7*b^5*Pi^3) + (x^6*Cos[(b^2*Pi*x^2)/2])/(7*b*Pi) + (x^7*FresnelS[b*x])/7 + (48*Sin[(b^2*Pi*x^2)/2])/(7*b^7*Pi^4) - (6*x^4*Sin[(b^2*Pi*x^2)/2])/(7*b^3*Pi^2)","A",6,4,8,0.5000,1,"{6426, 3379, 3296, 2637}"
3,1,99,0,0.0643839,"\int x^5 S(b x) \, dx","Int[x^5*FresnelS[b*x],x]","\frac{5 \text{FresnelC}(b x)}{2 \pi ^3 b^6}-\frac{5 x^3 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 \pi ^2 b^3}+\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{1}{6} x^6 S(b x)","\frac{5 \text{FresnelC}(b x)}{2 \pi ^3 b^6}-\frac{5 x^3 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 \pi ^2 b^3}+\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{1}{6} x^6 S(b x)",1,"(-5*x*Cos[(b^2*Pi*x^2)/2])/(2*b^5*Pi^3) + (x^5*Cos[(b^2*Pi*x^2)/2])/(6*b*Pi) + (5*FresnelC[b*x])/(2*b^6*Pi^3) + (x^6*FresnelS[b*x])/6 - (5*x^3*Sin[(b^2*Pi*x^2)/2])/(6*b^3*Pi^2)","A",5,4,8,0.5000,1,"{6426, 3385, 3386, 3352}"
4,1,84,0,0.0801435,"\int x^4 S(b x) \, dx","Int[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{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{1}{5} x^5 S(b x)","-\frac{4 x^2 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 \pi ^2 b^3}+\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{1}{5} x^5 S(b x)",1,"(-8*Cos[(b^2*Pi*x^2)/2])/(5*b^5*Pi^3) + (x^4*Cos[(b^2*Pi*x^2)/2])/(5*b*Pi) + (x^5*FresnelS[b*x])/5 - (4*x^2*Sin[(b^2*Pi*x^2)/2])/(5*b^3*Pi^2)","A",5,4,8,0.5000,1,"{6426, 3379, 3296, 2638}"
5,1,74,0,0.0474889,"\int x^3 S(b x) \, dx","Int[x^3*FresnelS[b*x],x]","\frac{3 S(b x)}{4 \pi ^2 b^4}-\frac{3 x \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi ^2 b^3}+\frac{x^3 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi  b}+\frac{1}{4} x^4 S(b x)","\frac{3 S(b x)}{4 \pi ^2 b^4}-\frac{3 x \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi ^2 b^3}+\frac{x^3 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi  b}+\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",4,4,8,0.5000,1,"{6426, 3385, 3386, 3351}"
6,1,59,0,0.052703,"\int x^2 S(b x) \, dx","Int[x^2*FresnelS[b*x],x]","-\frac{2 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 \pi ^2 b^3}+\frac{x^2 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 \pi  b}+\frac{1}{3} x^3 S(b x)","-\frac{2 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 \pi ^2 b^3}+\frac{x^2 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 \pi  b}+\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",4,4,8,0.5000,1,"{6426, 3379, 3296, 2637}"
7,1,49,0,0.0240392,"\int x S(b x) \, dx","Int[x*FresnelS[b*x],x]","-\frac{\text{FresnelC}(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{\text{FresnelC}(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",3,3,6,0.5000,1,"{6426, 3385, 3352}"
8,1,26,0,0.0048741,"\int S(b x) \, dx","Int[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",1,1,4,0.2500,1,"{6418}"
9,1,73,0,0.0466434,"\int \frac{S(b x)}{x} \, dx","Int[FresnelS[b*x]/x,x]","\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)","\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,"(I/2)*b*x*HypergeometricPFQ[{1/2, 1/2}, {3/2, 3/2}, (-I/2)*b^2*Pi*x^2] - (I/2)*b*x*HypergeometricPFQ[{1/2, 1/2}, {3/2, 3/2}, (I/2)*b^2*Pi*x^2]","A",3,3,8,0.3750,1,"{6424, 6358, 6360}"
10,1,27,0,0.0215755,"\int \frac{S(b x)}{x^2} \, dx","Int[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",2,2,8,0.2500,1,"{6426, 3375}"
11,1,44,0,0.0287987,"\int \frac{S(b x)}{x^3} \, dx","Int[FresnelS[b*x]/x^3,x]","\frac{1}{2} \pi  b^2 \text{FresnelC}(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 \text{FresnelC}(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",3,3,8,0.3750,1,"{6426, 3387, 3352}"
12,1,52,0,0.0637342,"\int \frac{S(b x)}{x^4} \, dx","Int[FresnelS[b*x]/x^4,x]","\frac{1}{12} \pi  b^3 \text{CosIntegral}\left(\frac{1}{2} \pi  b^2 x^2\right)-\frac{b \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 x^2}-\frac{S(b x)}{3 x^3}","\frac{1}{12} \pi  b^3 \text{CosIntegral}\left(\frac{1}{2} \pi  b^2 x^2\right)-\frac{b \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 x^2}-\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",4,4,8,0.5000,1,"{6426, 3379, 3297, 3302}"
13,1,69,0,0.0433676,"\int \frac{S(b x)}{x^5} \, dx","Int[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,"-(b^3*Pi*Cos[(b^2*Pi*x^2)/2])/(12*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",4,4,8,0.5000,1,"{6426, 3387, 3388, 3351}"
14,1,77,0,0.0892369,"\int \frac{S(b x)}{x^6} \, dx","Int[FresnelS[b*x]/x^6,x]","-\frac{1}{80} \pi ^2 b^5 \text{Si}\left(\frac{1}{2} b^2 \pi  x^2\right)-\frac{b \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{20 x^4}-\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{1}{80} \pi ^2 b^5 \text{Si}\left(\frac{1}{2} b^2 \pi  x^2\right)-\frac{b \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{20 x^4}-\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,"-(b^3*Pi*Cos[(b^2*Pi*x^2)/2])/(40*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",5,4,8,0.5000,1,"{6426, 3379, 3297, 3299}"
15,1,94,0,0.0593807,"\int \frac{S(b x)}{x^7} \, dx","Int[FresnelS[b*x]/x^7,x]","-\frac{1}{90} \pi ^3 b^6 \text{FresnelC}(b x)+\frac{\pi ^2 b^5 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{90 x}-\frac{b \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{30 x^5}-\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}","-\frac{1}{90} \pi ^3 b^6 \text{FresnelC}(b x)+\frac{\pi ^2 b^5 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{90 x}-\frac{b \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{30 x^5}-\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])/(90*x^3) - (b^6*Pi^3*FresnelC[b*x])/90 - FresnelS[b*x]/(6*x^6) - (b*Sin[(b^2*Pi*x^2)/2])/(30*x^5) + (b^5*Pi^2*Sin[(b^2*Pi*x^2)/2])/(90*x)","A",5,4,8,0.5000,1,"{6426, 3387, 3388, 3352}"
16,1,102,0,0.1215326,"\int \frac{S(b x)}{x^8} \, dx","Int[FresnelS[b*x]/x^8,x]","-\frac{1}{672} \pi ^3 b^7 \text{CosIntegral}\left(\frac{1}{2} \pi  b^2 x^2\right)+\frac{\pi ^2 b^5 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{336 x^2}-\frac{b \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{42 x^6}-\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}","-\frac{1}{672} \pi ^3 b^7 \text{CosIntegral}\left(\frac{1}{2} \pi  b^2 x^2\right)+\frac{\pi ^2 b^5 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{336 x^2}-\frac{b \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{42 x^6}-\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,"-(b^3*Pi*Cos[(b^2*Pi*x^2)/2])/(168*x^4) - (b^7*Pi^3*CosIntegral[(b^2*Pi*x^2)/2])/672 - FresnelS[b*x]/(7*x^7) - (b*Sin[(b^2*Pi*x^2)/2])/(42*x^6) + (b^5*Pi^2*Sin[(b^2*Pi*x^2)/2])/(336*x^2)","A",6,4,8,0.5000,1,"{6426, 3379, 3297, 3302}"
17,1,119,0,0.0810103,"\int \frac{S(b x)}{x^9} \, dx","Int[FresnelS[b*x]/x^9,x]","\frac{1}{840} \pi ^4 b^8 S(b x)+\frac{\pi ^2 b^5 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{840 x^3}-\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  b^3 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{280 x^5}-\frac{S(b x)}{8 x^8}","\frac{1}{840} \pi ^4 b^8 S(b x)+\frac{\pi ^2 b^5 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{840 x^3}-\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  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*Cos[(b^2*Pi*x^2)/2])/(280*x^5) + (b^7*Pi^3*Cos[(b^2*Pi*x^2)/2])/(840*x) + (b^8*Pi^4*FresnelS[b*x])/840 - FresnelS[b*x]/(8*x^8) - (b*Sin[(b^2*Pi*x^2)/2])/(56*x^7) + (b^5*Pi^2*Sin[(b^2*Pi*x^2)/2])/(840*x^3)","A",6,4,8,0.5000,1,"{6426, 3387, 3388, 3351}"
18,1,127,0,0.1529541,"\int \frac{S(b x)}{x^{10}} \, dx","Int[FresnelS[b*x]/x^10,x]","\frac{\pi ^4 b^9 \text{Si}\left(\frac{1}{2} b^2 \pi  x^2\right)}{6912}+\frac{\pi ^2 b^5 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{1728 x^4}-\frac{b \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{72 x^8}+\frac{\pi ^3 b^7 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{3456 x^2}-\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}","\frac{\pi ^4 b^9 \text{Si}\left(\frac{1}{2} b^2 \pi  x^2\right)}{6912}+\frac{\pi ^2 b^5 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{1728 x^4}-\frac{b \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{72 x^8}+\frac{\pi ^3 b^7 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{3456 x^2}-\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,"-(b^3*Pi*Cos[(b^2*Pi*x^2)/2])/(432*x^6) + (b^7*Pi^3*Cos[(b^2*Pi*x^2)/2])/(3456*x^2) - FresnelS[b*x]/(9*x^9) - (b*Sin[(b^2*Pi*x^2)/2])/(72*x^8) + (b^5*Pi^2*Sin[(b^2*Pi*x^2)/2])/(1728*x^4) + (b^9*Pi^4*SinIntegral[(b^2*Pi*x^2)/2])/6912","A",7,4,8,0.5000,1,"{6426, 3379, 3297, 3299}"
19,1,296,0,0.400987,"\int (c+d x)^3 S(a+b x) \, dx","Int[(c + d*x)^3*FresnelS[a + b*x],x]","-\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 \text{FresnelC}(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}","-\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 \text{FresnelC}(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,"((b*c - a*d)^3*Cos[(Pi*(a + b*x)^2)/2])/(b^4*Pi) + (3*d*(b*c - a*d)^2*(a + b*x)*Cos[(Pi*(a + b*x)^2)/2])/(2*b^4*Pi) + (d^2*(b*c - a*d)*(a + b*x)^2*Cos[(Pi*(a + b*x)^2)/2])/(b^4*Pi) + (d^3*(a + b*x)^3*Cos[(Pi*(a + b*x)^2)/2])/(4*b^4*Pi) - (3*d*(b*c - a*d)^2*FresnelC[a + b*x])/(2*b^4*Pi) - ((b*c - a*d)^4*FresnelS[a + b*x])/(4*b^4*d) + (3*d^3*FresnelS[a + b*x])/(4*b^4*Pi^2) + ((c + d*x)^4*FresnelS[a + b*x])/(4*d) - (2*d^2*(b*c - a*d)*Sin[(Pi*(a + b*x)^2)/2])/(b^4*Pi^2) - (3*d^3*(a + b*x)*Sin[(Pi*(a + b*x)^2)/2])/(4*b^4*Pi^2)","A",14,10,14,0.7143,1,"{6428, 3433, 3351, 3379, 2638, 3385, 3352, 3296, 2637, 3386}"
20,1,193,0,0.2257432,"\int (c+d x)^2 S(a+b x) \, dx","Int[(c + d*x)^2*FresnelS[a + b*x],x]","-\frac{d (b c-a d) \text{FresnelC}(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}","-\frac{d (b c-a d) \text{FresnelC}(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,"((b*c - a*d)^2*Cos[(Pi*(a + b*x)^2)/2])/(b^3*Pi) + (d*(b*c - a*d)*(a + b*x)*Cos[(Pi*(a + b*x)^2)/2])/(b^3*Pi) + (d^2*(a + b*x)^2*Cos[(Pi*(a + b*x)^2)/2])/(3*b^3*Pi) - (d*(b*c - a*d)*FresnelC[a + b*x])/(b^3*Pi) - ((b*c - a*d)^3*FresnelS[a + b*x])/(3*b^3*d) + ((c + d*x)^3*FresnelS[a + b*x])/(3*d) - (2*d^2*Sin[(Pi*(a + b*x)^2)/2])/(3*b^3*Pi^2)","A",11,9,14,0.6429,1,"{6428, 3433, 3351, 3379, 2638, 3385, 3352, 3296, 2637}"
21,1,121,0,0.1144995,"\int (c+d x) S(a+b x) \, dx","Int[(c + d*x)*FresnelS[a + b*x],x]","-\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 \text{FresnelC}(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}","-\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 \text{FresnelC}(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,"((b*c - a*d)*Cos[(Pi*(a + b*x)^2)/2])/(b^2*Pi) + (d*(a + b*x)*Cos[(Pi*(a + b*x)^2)/2])/(2*b^2*Pi) - (d*FresnelC[a + b*x])/(2*b^2*Pi) - ((b*c - a*d)^2*FresnelS[a + b*x])/(2*b^2*d) + ((c + d*x)^2*FresnelS[a + b*x])/(2*d)","A",8,7,12,0.5833,1,"{6428, 3433, 3351, 3379, 2638, 3385, 3352}"
22,1,36,0,0.0063385,"\int S(a+b x) \, dx","Int[FresnelS[a + b*x],x]","\frac{(a+b x) S(a+b x)}{b}+\frac{\cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  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[(Pi*(a + b*x)^2)/2]/(b*Pi) + ((a + b*x)*FresnelS[a + b*x])/b","A",1,1,6,0.1667,1,"{6418}"
23,0,0,0,0.0146781,"\int \frac{S(a+b x)}{c+d x} \, dx","Int[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,"Defer[Int][FresnelS[a + b*x]/(c + d*x), x]","A",0,0,0,0,-1,"{}"
24,0,0,0,0.0142623,"\int \frac{S(a+b x)}{(c+d x)^2} \, dx","Int[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,"Defer[Int][FresnelS[a + b*x]/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
25,1,229,0,0.1844514,"\int x^3 S(a+b x) \, dx","Int[x^3*FresnelS[a + b*x],x]","-\frac{3 a^2 \text{FresnelC}(a+b x)}{2 \pi  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 (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)","-\frac{3 a^2 \text{FresnelC}(a+b x)}{2 \pi  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 (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*Cos[(Pi*(a + b*x)^2)/2])/(b^4*Pi)) + (3*a^2*(a + b*x)*Cos[(Pi*(a + b*x)^2)/2])/(2*b^4*Pi) - (a*(a + b*x)^2*Cos[(Pi*(a + b*x)^2)/2])/(b^4*Pi) + ((a + b*x)^3*Cos[(Pi*(a + b*x)^2)/2])/(4*b^4*Pi) - (3*a^2*FresnelC[a + b*x])/(2*b^4*Pi) - (a^4*FresnelS[a + b*x])/(4*b^4) + (3*FresnelS[a + b*x])/(4*b^4*Pi^2) + (x^4*FresnelS[a + b*x])/4 + (2*a*Sin[(Pi*(a + b*x)^2)/2])/(b^4*Pi^2) - (3*(a + b*x)*Sin[(Pi*(a + b*x)^2)/2])/(4*b^4*Pi^2)","A",14,10,10,1.000,1,"{6428, 3433, 3351, 3379, 2638, 3385, 3352, 3296, 2637, 3386}"
26,1,147,0,0.1286831,"\int x^2 S(a+b x) \, dx","Int[x^2*FresnelS[a + b*x],x]","\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 \text{FresnelC}(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)","\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 \text{FresnelC}(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*Cos[(Pi*(a + b*x)^2)/2])/(b^3*Pi) - (a*(a + b*x)*Cos[(Pi*(a + b*x)^2)/2])/(b^3*Pi) + ((a + b*x)^2*Cos[(Pi*(a + b*x)^2)/2])/(3*b^3*Pi) + (a*FresnelC[a + b*x])/(b^3*Pi) + (a^3*FresnelS[a + b*x])/(3*b^3) + (x^3*FresnelS[a + b*x])/3 - (2*Sin[(Pi*(a + b*x)^2)/2])/(3*b^3*Pi^2)","A",11,9,10,0.9000,1,"{6428, 3433, 3351, 3379, 2638, 3385, 3352, 3296, 2637}"
27,1,96,0,0.0672627,"\int x S(a+b x) \, dx","Int[x*FresnelS[a + b*x],x]","-\frac{a^2 S(a+b x)}{2 b^2}-\frac{\text{FresnelC}(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)","-\frac{a^2 S(a+b x)}{2 b^2}-\frac{\text{FresnelC}(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,"-((a*Cos[(Pi*(a + b*x)^2)/2])/(b^2*Pi)) + ((a + b*x)*Cos[(Pi*(a + b*x)^2)/2])/(2*b^2*Pi) - FresnelC[a + b*x]/(2*b^2*Pi) - (a^2*FresnelS[a + b*x])/(2*b^2) + (x^2*FresnelS[a + b*x])/2","A",8,7,8,0.8750,1,"{6428, 3433, 3351, 3379, 2638, 3385, 3352}"
28,1,36,0,0.0065408,"\int S(a+b x) \, dx","Int[FresnelS[a + b*x],x]","\frac{(a+b x) S(a+b x)}{b}+\frac{\cos \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  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[(Pi*(a + b*x)^2)/2]/(b*Pi) + ((a + b*x)*FresnelS[a + b*x])/b","A",1,1,6,0.1667,1,"{6418}"
29,0,0,0,0.0105536,"\int \frac{S(a+b x)}{x} \, dx","Int[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,"Defer[Int][FresnelS[a + b*x]/x, x]","A",0,0,0,0,-1,"{}"
30,0,0,0,0.0112494,"\int \frac{S(a+b x)}{x^2} \, dx","Int[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,"Defer[Int][FresnelS[a + b*x]/x^2, x]","A",0,0,0,0,-1,"{}"
31,1,253,0,0.4284151,"\int x^7 S(b x)^2 \, dx","Int[x^7*FresnelS[b*x]^2,x]","-\frac{7 x^5 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi ^2 b^3}+\frac{105 x S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi ^4 b^7}+\frac{x^7 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi  b}-\frac{35 x^3 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi ^3 b^5}-\frac{105 S(b x)^2}{8 \pi ^4 b^8}+\frac{7 x^6}{48 \pi ^2 b^2}-\frac{105 x^2}{16 \pi ^4 b^6}-\frac{5 x^4 \sin \left(\pi  b^2 x^2\right)}{8 \pi ^3 b^4}+\frac{10 \sin \left(\pi  b^2 x^2\right)}{\pi ^5 b^8}+\frac{x^6 \cos \left(\pi  b^2 x^2\right)}{16 \pi ^2 b^2}-\frac{55 x^2 \cos \left(\pi  b^2 x^2\right)}{16 \pi ^4 b^6}+\frac{1}{8} x^8 S(b x)^2","-\frac{7 x^5 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi ^2 b^3}+\frac{105 x S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi ^4 b^7}+\frac{x^7 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi  b}-\frac{35 x^3 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi ^3 b^5}-\frac{105 S(b x)^2}{8 \pi ^4 b^8}+\frac{7 x^6}{48 \pi ^2 b^2}-\frac{105 x^2}{16 \pi ^4 b^6}-\frac{5 x^4 \sin \left(\pi  b^2 x^2\right)}{8 \pi ^3 b^4}+\frac{10 \sin \left(\pi  b^2 x^2\right)}{\pi ^5 b^8}+\frac{x^6 \cos \left(\pi  b^2 x^2\right)}{16 \pi ^2 b^2}-\frac{55 x^2 \cos \left(\pi  b^2 x^2\right)}{16 \pi ^4 b^6}+\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",23,10,10,1.000,1,"{6430, 6454, 6462, 3379, 3309, 30, 3296, 2637, 2634, 6440}"
32,1,239,0,0.3178915,"\int x^6 S(b x)^2 \, dx","Int[x^6*FresnelS[b*x]^2,x]","\frac{531 \text{FresnelC}\left(\sqrt{2} b x\right)}{56 \sqrt{2} \pi ^4 b^7}-\frac{12 x^4 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi ^2 b^3}+\frac{96 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi ^4 b^7}+\frac{2 x^6 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi  b}-\frac{48 x^2 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi ^3 b^5}+\frac{6 x^5}{35 \pi ^2 b^2}-\frac{17 x^3 \sin \left(\pi  b^2 x^2\right)}{28 \pi ^3 b^4}+\frac{x^5 \cos \left(\pi  b^2 x^2\right)}{14 \pi ^2 b^2}-\frac{21 x \cos \left(\pi  b^2 x^2\right)}{8 \pi ^4 b^6}-\frac{48 x}{7 \pi ^4 b^6}+\frac{1}{7} x^7 S(b x)^2","\frac{531 \text{FresnelC}\left(\sqrt{2} b x\right)}{56 \sqrt{2} \pi ^4 b^7}-\frac{12 x^4 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi ^2 b^3}+\frac{96 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi ^4 b^7}+\frac{2 x^6 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi  b}-\frac{48 x^2 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi ^3 b^5}+\frac{6 x^5}{35 \pi ^2 b^2}-\frac{17 x^3 \sin \left(\pi  b^2 x^2\right)}{28 \pi ^3 b^4}+\frac{x^5 \cos \left(\pi  b^2 x^2\right)}{14 \pi ^2 b^2}-\frac{21 x \cos \left(\pi  b^2 x^2\right)}{8 \pi ^4 b^6}-\frac{48 x}{7 \pi ^4 b^6}+\frac{1}{7} x^7 S(b x)^2",1,"(-48*x)/(7*b^6*Pi^4) + (6*x^5)/(35*b^2*Pi^2) - (21*x*Cos[b^2*Pi*x^2])/(8*b^6*Pi^4) + (x^5*Cos[b^2*Pi*x^2])/(14*b^2*Pi^2) + (531*FresnelC[Sqrt[2]*b*x])/(56*Sqrt[2]*b^7*Pi^4) - (48*x^2*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(7*b^5*Pi^3) + (2*x^6*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(7*b*Pi) + (x^7*FresnelS[b*x]^2)/7 + (96*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(7*b^7*Pi^4) - (12*x^4*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(7*b^3*Pi^2) - (17*x^3*Sin[b^2*Pi*x^2])/(28*b^4*Pi^3)","A",19,10,10,1.000,1,"{6430, 6454, 6462, 3391, 30, 3386, 3385, 3352, 6460, 3357}"
33,1,265,0,0.3000673,"\int x^5 S(b x)^2 \, dx","Int[x^5*FresnelS[b*x]^2,x]","-\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 \text{FresnelC}(b x) S(b x)}{2 \pi ^3 b^6}-\frac{5 x^3 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 \pi ^2 b^3}+\frac{x^5 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 \pi  b}-\frac{5 x S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^5}+\frac{5 x^4}{24 \pi ^2 b^2}-\frac{7 x^2 \sin \left(\pi  b^2 x^2\right)}{12 \pi ^3 b^4}+\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{1}{6} x^6 S(b x)^2","-\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 \text{FresnelC}(b x) S(b x)}{2 \pi ^3 b^6}-\frac{5 x^3 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 \pi ^2 b^3}+\frac{x^5 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 \pi  b}-\frac{5 x S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^5}+\frac{5 x^4}{24 \pi ^2 b^2}-\frac{7 x^2 \sin \left(\pi  b^2 x^2\right)}{12 \pi ^3 b^4}+\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{1}{6} x^6 S(b x)^2",1,"(5*x^4)/(24*b^2*Pi^2) - (11*Cos[b^2*Pi*x^2])/(6*b^6*Pi^4) + (x^4*Cos[b^2*Pi*x^2])/(12*b^2*Pi^2) - (5*x*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(b^5*Pi^3) + (x^5*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(3*b*Pi) + (5*FresnelC[b*x]*FresnelS[b*x])/(2*b^6*Pi^3) + (x^6*FresnelS[b*x]^2)/6 - (((5*I)/8)*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (-I/2)*b^2*Pi*x^2])/(b^4*Pi^3) + (((5*I)/8)*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (I/2)*b^2*Pi*x^2])/(b^4*Pi^3) - (5*x^3*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(3*b^3*Pi^2) - (7*x^2*Sin[b^2*Pi*x^2])/(12*b^4*Pi^3)","A",16,9,10,0.9000,1,"{6430, 6454, 6462, 3379, 3309, 30, 3296, 2638, 6446}"
34,1,177,0,0.1877537,"\int x^4 S(b x)^2 \, dx","Int[x^4*FresnelS[b*x]^2,x]","-\frac{8 x^2 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 \pi ^2 b^3}+\frac{2 x^4 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 \pi  b}-\frac{16 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 \pi ^3 b^5}+\frac{43 S\left(\sqrt{2} b x\right)}{20 \sqrt{2} \pi ^3 b^5}+\frac{4 x^3}{15 \pi ^2 b^2}-\frac{11 x \sin \left(\pi  b^2 x^2\right)}{20 \pi ^3 b^4}+\frac{x^3 \cos \left(\pi  b^2 x^2\right)}{10 \pi ^2 b^2}+\frac{1}{5} x^5 S(b x)^2","-\frac{8 x^2 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 \pi ^2 b^3}+\frac{2 x^4 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 \pi  b}-\frac{16 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 \pi ^3 b^5}+\frac{43 S\left(\sqrt{2} b x\right)}{20 \sqrt{2} \pi ^3 b^5}+\frac{4 x^3}{15 \pi ^2 b^2}-\frac{11 x \sin \left(\pi  b^2 x^2\right)}{20 \pi ^3 b^4}+\frac{x^3 \cos \left(\pi  b^2 x^2\right)}{10 \pi ^2 b^2}+\frac{1}{5} x^5 S(b x)^2",1,"(4*x^3)/(15*b^2*Pi^2) + (x^3*Cos[b^2*Pi*x^2])/(10*b^2*Pi^2) - (16*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(5*b^5*Pi^3) + (2*x^4*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(5*b*Pi) + (x^5*FresnelS[b*x]^2)/5 + (43*FresnelS[Sqrt[2]*b*x])/(20*Sqrt[2]*b^5*Pi^3) - (8*x^2*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(5*b^3*Pi^2) - (11*x*Sin[b^2*Pi*x^2])/(20*b^4*Pi^3)","A",12,9,10,0.9000,1,"{6430, 6454, 6462, 3391, 30, 3386, 3351, 6452, 3385}"
35,1,140,0,0.1508779,"\int x^3 S(b x)^2 \, dx","Int[x^3*FresnelS[b*x]^2,x]","-\frac{3 x S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{2 \pi ^2 b^3}+\frac{x^3 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{2 \pi  b}+\frac{3 S(b x)^2}{4 \pi ^2 b^4}+\frac{3 x^2}{8 \pi ^2 b^2}-\frac{\sin \left(\pi  b^2 x^2\right)}{2 \pi ^3 b^4}+\frac{x^2 \cos \left(\pi  b^2 x^2\right)}{8 \pi ^2 b^2}+\frac{1}{4} x^4 S(b x)^2","-\frac{3 x S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{2 \pi ^2 b^3}+\frac{x^3 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{2 \pi  b}+\frac{3 S(b x)^2}{4 \pi ^2 b^4}+\frac{3 x^2}{8 \pi ^2 b^2}-\frac{\sin \left(\pi  b^2 x^2\right)}{2 \pi ^3 b^4}+\frac{x^2 \cos \left(\pi  b^2 x^2\right)}{8 \pi ^2 b^2}+\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",10,9,10,0.9000,1,"{6430, 6454, 6462, 3379, 2634, 6440, 30, 3296, 2637}"
36,1,124,0,0.1108757,"\int x^2 S(b x)^2 \, dx","Int[x^2*FresnelS[b*x]^2,x]","-\frac{5 \text{FresnelC}\left(\sqrt{2} b x\right)}{6 \sqrt{2} \pi ^2 b^3}-\frac{4 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 \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{1}{3} x^3 S(b x)^2","-\frac{5 \text{FresnelC}\left(\sqrt{2} b x\right)}{6 \sqrt{2} \pi ^2 b^3}-\frac{4 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 \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{1}{3} x^3 S(b x)^2",1,"(2*x)/(3*b^2*Pi^2) + (x*Cos[b^2*Pi*x^2])/(6*b^2*Pi^2) - (5*FresnelC[Sqrt[2]*b*x])/(6*Sqrt[2]*b^3*Pi^2) + (2*x^2*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(3*b*Pi) + (x^3*FresnelS[b*x]^2)/3 - (4*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(3*b^3*Pi^2)","A",8,6,10,0.6000,1,"{6430, 6454, 6460, 3357, 3352, 3385}"
37,1,143,0,0.0863939,"\int x S(b x)^2 \, dx","Int[x*FresnelS[b*x]^2,x]","\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{\text{FresnelC}(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","\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{\text{FresnelC}(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,"Cos[b^2*Pi*x^2]/(4*b^2*Pi^2) + (x*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(b*Pi) - (FresnelC[b*x]*FresnelS[b*x])/(2*b^2*Pi) + (x^2*FresnelS[b*x]^2)/2 + ((I/8)*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (-I/2)*b^2*Pi*x^2])/Pi - ((I/8)*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (I/2)*b^2*Pi*x^2])/Pi","A",5,5,8,0.6250,1,"{6430, 6454, 6446, 3379, 2638}"
38,1,55,0,0.0383974,"\int S(b x)^2 \, dx","Int[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",4,4,6,0.6667,1,"{6420, 12, 6452, 3351}"
39,0,0,0,0.0166764,"\int \frac{S(b x)^2}{x} \, dx","Int[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,"Defer[Int][FresnelS[b*x]^2/x, x]","A",0,0,0,0,-1,"{}"
40,0,0,0,0.0372656,"\int \frac{S(b x)^2}{x^2} \, dx","Int[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,"-(FresnelS[b*x]^2/x) + 2*b*Defer[Int][(FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/x, x]","A",0,0,0,0,-1,"{}"
41,0,0,0,0.0383717,"\int \frac{S(b x)^2}{x^3} \, dx","Int[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,"-FresnelS[b*x]^2/(2*x^2) + b*Defer[Int][(FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/x^2, x]","A",0,0,0,0,-1,"{}"
42,0,0,0,0.0873615,"\int \frac{S(b x)^2}{x^4} \, dx","Int[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{b S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 x^2}+\frac{\pi  b^3 S\left(\sqrt{2} b x\right)}{3 \sqrt{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,"-b^2/(6*x) + (b^2*Cos[b^2*Pi*x^2])/(6*x) - FresnelS[b*x]^2/(3*x^3) + (b^3*Pi*FresnelS[Sqrt[2]*b*x])/(3*Sqrt[2]) - (b*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(3*x^2) + (b^3*Pi*Defer[Int][(Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/x, x])/3","A",0,0,0,0,-1,"{}"
43,1,127,0,0.1431535,"\int \frac{S(b x)^2}{x^5} \, dx","Int[FresnelS[b*x]^2/x^5,x]","-\frac{b S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 x^3}-\frac{\pi  b^3 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 x}-\frac{1}{12} \pi ^2 b^4 S(b x)^2+\frac{1}{12} \pi  b^4 \text{Si}\left(b^2 \pi  x^2\right)-\frac{b^2}{24 x^2}+\frac{b^2 \cos \left(\pi  b^2 x^2\right)}{24 x^2}-\frac{S(b x)^2}{4 x^4}","-\frac{b S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 x^3}-\frac{\pi  b^3 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 x}-\frac{1}{12} \pi ^2 b^4 S(b x)^2+\frac{1}{12} \pi  b^4 \text{Si}\left(b^2 \pi  x^2\right)-\frac{b^2}{24 x^2}+\frac{b^2 \cos \left(\pi  b^2 x^2\right)}{24 x^2}-\frac{S(b x)^2}{4 x^4}",1,"-b^2/(24*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",9,9,10,0.9000,1,"{6430, 6456, 6464, 6440, 30, 3375, 3380, 3297, 3299}"
44,0,0,0,0.1538463,"\int \frac{S(b x)^2}{x^6} \, dx","Int[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 \text{FresnelC}\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{\pi  b^3 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{20 x^2}-\frac{b^2}{60 x^3}-\frac{7 \pi  b^4 \sin \left(\pi  b^2 x^2\right)}{120 x}+\frac{b^2 \cos \left(\pi  b^2 x^2\right)}{60 x^3}-\frac{S(b x)^2}{5 x^5}",0,"-b^2/(60*x^3) + (b^2*Cos[b^2*Pi*x^2])/(60*x^3) + (7*b^5*Pi^2*FresnelC[Sqrt[2]*b*x])/(60*Sqrt[2]) - (b^3*Pi*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(20*x^2) - FresnelS[b*x]^2/(5*x^5) - (b*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(10*x^4) - (7*b^4*Pi*Sin[b^2*Pi*x^2])/(120*x) - (b^5*Pi^2*Defer[Int][(FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/x, x])/20","A",0,0,0,0,-1,"{}"
45,0,0,0,0.2220545,"\int \frac{S(b x)^2}{x^7} \, dx","Int[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{1}{72} \pi ^2 b^6 \text{CosIntegral}\left(\pi  b^2 x^2\right)-\frac{b S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{15 x^5}-\frac{\pi  b^3 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{45 x^3}-\frac{b^2}{120 x^4}-\frac{\pi  b^4 \sin \left(\pi  b^2 x^2\right)}{72 x^2}+\frac{b^2 \cos \left(\pi  b^2 x^2\right)}{120 x^4}-\frac{S(b x)^2}{6 x^6}",0,"-b^2/(120*x^4) + (b^2*Cos[b^2*Pi*x^2])/(120*x^4) + (b^6*Pi^2*CosIntegral[b^2*Pi*x^2])/72 - (b^3*Pi*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(45*x^3) - FresnelS[b*x]^2/(6*x^6) - (b*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(15*x^5) - (b^4*Pi*Sin[b^2*Pi*x^2])/(72*x^2) - (b^5*Pi^2*Defer[Int][(FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/x^2, x])/45","A",0,0,0,0,-1,"{}"
46,0,0,0,0.2445563,"\int \frac{S(b x)^2}{x^8} \, dx","Int[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{\pi ^2 b^5 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{168 x^2}-\frac{b S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{21 x^6}-\frac{\pi  b^3 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{84 x^4}-\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{b^2}{210 x^5}-\frac{13 \pi  b^4 \sin \left(\pi  b^2 x^2\right)}{2520 x^3}-\frac{67 \pi ^2 b^6 \cos \left(\pi  b^2 x^2\right)}{5040 x}+\frac{b^2 \cos \left(\pi  b^2 x^2\right)}{210 x^5}+\frac{\pi ^2 b^6}{336 x}-\frac{S(b x)^2}{7 x^7}",0,"-b^2/(210*x^5) + (b^6*Pi^2)/(336*x) + (b^2*Cos[b^2*Pi*x^2])/(210*x^5) - (67*b^6*Pi^2*Cos[b^2*Pi*x^2])/(5040*x) - (b^3*Pi*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(84*x^4) - FresnelS[b*x]^2/(7*x^7) - (b^7*Pi^3*FresnelS[Sqrt[2]*b*x])/(72*Sqrt[2]) - (2*Sqrt[2]*b^7*Pi^3*FresnelS[Sqrt[2]*b*x])/315 - (b*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(21*x^6) + (b^5*Pi^2*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(168*x^2) - (13*b^4*Pi*Sin[b^2*Pi*x^2])/(2520*x^3) - (b^7*Pi^3*Defer[Int][(Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/x, x])/168","A",0,0,0,0,-1,"{}"
47,1,242,0,0.3930466,"\int \frac{S(b x)^2}{x^9} \, dx","Int[FresnelS[b*x]^2/x^9,x]","\frac{\pi ^2 b^5 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{420 x^3}-\frac{b S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{28 x^7}+\frac{\pi ^3 b^7 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{420 x}-\frac{\pi  b^3 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{140 x^5}+\frac{1}{840} \pi ^4 b^8 S(b x)^2-\frac{1}{280} \pi ^3 b^8 \text{Si}\left(b^2 \pi  x^2\right)+\frac{\pi ^2 b^6}{1680 x^2}-\frac{b^2}{336 x^6}-\frac{\pi  b^4 \sin \left(\pi  b^2 x^2\right)}{420 x^4}-\frac{\pi ^2 b^6 \cos \left(\pi  b^2 x^2\right)}{336 x^2}+\frac{b^2 \cos \left(\pi  b^2 x^2\right)}{336 x^6}-\frac{S(b x)^2}{8 x^8}","\frac{\pi ^2 b^5 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{420 x^3}-\frac{b S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{28 x^7}+\frac{\pi ^3 b^7 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{420 x}-\frac{\pi  b^3 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{140 x^5}+\frac{1}{840} \pi ^4 b^8 S(b x)^2-\frac{1}{280} \pi ^3 b^8 \text{Si}\left(b^2 \pi  x^2\right)+\frac{\pi ^2 b^6}{1680 x^2}-\frac{b^2}{336 x^6}-\frac{\pi  b^4 \sin \left(\pi  b^2 x^2\right)}{420 x^4}-\frac{\pi ^2 b^6 \cos \left(\pi  b^2 x^2\right)}{336 x^2}+\frac{b^2 \cos \left(\pi  b^2 x^2\right)}{336 x^6}-\frac{S(b x)^2}{8 x^8}",1,"-b^2/(336*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",20,10,10,1.000,1,"{6430, 6456, 6464, 6440, 30, 3375, 3380, 3297, 3299, 3379}"
48,0,0,0,0.3583173,"\int \frac{S(b x)^2}{x^{10}} \, dx","Int[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 \text{FresnelC}\left(\sqrt{2} b x\right)}{181440 \sqrt{2}}+\frac{\pi ^2 b^5 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{864 x^4}-\frac{b S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{36 x^8}+\frac{\pi ^3 b^7 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{1728 x^2}-\frac{\pi  b^3 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{216 x^6}+\frac{\pi ^2 b^6}{5184 x^3}-\frac{b^2}{504 x^7}+\frac{853 \pi ^3 b^8 \sin \left(\pi  b^2 x^2\right)}{362880 x}-\frac{19 \pi  b^4 \sin \left(\pi  b^2 x^2\right)}{15120 x^5}-\frac{187 \pi ^2 b^6 \cos \left(\pi  b^2 x^2\right)}{181440 x^3}+\frac{b^2 \cos \left(\pi  b^2 x^2\right)}{504 x^7}-\frac{S(b x)^2}{9 x^9}",0,"-b^2/(504*x^7) + (b^6*Pi^2)/(5184*x^3) + (b^2*Cos[b^2*Pi*x^2])/(504*x^7) - (187*b^6*Pi^2*Cos[b^2*Pi*x^2])/(181440*x^3) - (853*b^9*Pi^4*FresnelC[Sqrt[2]*b*x])/(181440*Sqrt[2]) - (b^3*Pi*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(216*x^6) + (b^7*Pi^3*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(1728*x^2) - FresnelS[b*x]^2/(9*x^9) - (b*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(36*x^8) + (b^5*Pi^2*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(864*x^4) - (19*b^4*Pi*Sin[b^2*Pi*x^2])/(15120*x^5) + (853*b^8*Pi^3*Sin[b^2*Pi*x^2])/(362880*x) + (b^9*Pi^4*Defer[Int][(FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/x, x])/1728","A",0,0,0,0,-1,"{}"
49,1,497,0,0.410257,"\int (c+d x)^2 S(a+b x)^2 \, dx","Int[(c + d*x)^2*FresnelS[a + b*x]^2,x]","\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) \text{FresnelC}(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 \text{FresnelC}\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}","\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) \text{FresnelC}(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 \text{FresnelC}\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,"(2*d^2*x)/(3*b^2*Pi^2) + (d*(b*c - a*d)*Cos[Pi*(a + b*x)^2])/(2*b^3*Pi^2) + (d^2*(a + b*x)*Cos[Pi*(a + b*x)^2])/(6*b^3*Pi^2) - (5*d^2*FresnelC[Sqrt[2]*(a + b*x)])/(6*Sqrt[2]*b^3*Pi^2) + (2*(b*c - a*d)^2*Cos[(Pi*(a + b*x)^2)/2]*FresnelS[a + b*x])/(b^3*Pi) + (2*d*(b*c - a*d)*(a + b*x)*Cos[(Pi*(a + b*x)^2)/2]*FresnelS[a + b*x])/(b^3*Pi) + (2*d^2*(a + b*x)^2*Cos[(Pi*(a + b*x)^2)/2]*FresnelS[a + b*x])/(3*b^3*Pi) - (d*(b*c - a*d)*FresnelC[a + b*x]*FresnelS[a + b*x])/(b^3*Pi) + ((b*c - a*d)^2*(a + b*x)*FresnelS[a + b*x]^2)/b^3 + (d*(b*c - a*d)*(a + b*x)^2*FresnelS[a + b*x]^2)/b^3 + (d^2*(a + b*x)^3*FresnelS[a + b*x]^2)/(3*b^3) - ((b*c - a*d)^2*FresnelS[Sqrt[2]*(a + b*x)])/(Sqrt[2]*b^3*Pi) + ((I/4)*d*(b*c - a*d)*(a + b*x)^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (-I/2)*Pi*(a + b*x)^2])/(b^3*Pi) - ((I/4)*d*(b*c - a*d)*(a + b*x)^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (I/2)*Pi*(a + b*x)^2])/(b^3*Pi) - (4*d^2*FresnelS[a + b*x]*Sin[(Pi*(a + b*x)^2)/2])/(3*b^3*Pi^2)","A",18,13,16,0.8125,1,"{6432, 6420, 6452, 3351, 6430, 6454, 6446, 3379, 2638, 6460, 3357, 3352, 3385}"
50,1,279,0,0.196207,"\int (c+d x) S(a+b x)^2 \, dx","Int[(c + d*x)*FresnelS[a + b*x]^2,x]","\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 \text{FresnelC}(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}","\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 \text{FresnelC}(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,"(d*Cos[Pi*(a + b*x)^2])/(4*b^2*Pi^2) + (2*(b*c - a*d)*Cos[(Pi*(a + b*x)^2)/2]*FresnelS[a + b*x])/(b^2*Pi) + (d*(a + b*x)*Cos[(Pi*(a + b*x)^2)/2]*FresnelS[a + b*x])/(b^2*Pi) - (d*FresnelC[a + b*x]*FresnelS[a + b*x])/(2*b^2*Pi) + ((b*c - a*d)*(a + b*x)*FresnelS[a + b*x]^2)/b^2 + (d*(a + b*x)^2*FresnelS[a + b*x]^2)/(2*b^2) - ((b*c - a*d)*FresnelS[Sqrt[2]*(a + b*x)])/(Sqrt[2]*b^2*Pi) + ((I/8)*d*(a + b*x)^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (-I/2)*Pi*(a + b*x)^2])/(b^2*Pi) - ((I/8)*d*(a + b*x)^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (I/2)*Pi*(a + b*x)^2])/(b^2*Pi)","A",10,9,14,0.6429,1,"{6432, 6420, 6452, 3351, 6430, 6454, 6446, 3379, 2638}"
51,1,70,0,0.1677263,"\int S(a+b x)^2 \, dx","Int[FresnelS[a + b*x]^2,x]","\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}","\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,"(2*Cos[(Pi*(a + b*x)^2)/2]*FresnelS[a + b*x])/(b*Pi) + ((a + b*x)*FresnelS[a + b*x]^2)/b - FresnelS[Sqrt[2]*(a + b*x)]/(Sqrt[2]*b*Pi)","A",4,3,8,0.3750,1,"{6420, 6452, 3351}"
52,0,0,0,0.0232799,"\int \frac{S(a+b x)^2}{c+d x} \, dx","Int[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,"Defer[Int][FresnelS[a + b*x]^2/(c + d*x), x]","A",0,0,0,0,-1,"{}"
53,0,0,0,0.0228937,"\int \frac{S(a+b x)^2}{(c+d x)^2} \, dx","Int[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,"Defer[Int][FresnelS[a + b*x]^2/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
54,1,231,0,0.5705959,"\int x^2 S\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[x^2*FresnelS[d*(a + b*Log[c*x^n])],x]","\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)","\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,"((1/12 - I/12)*E^((-3*a)/(b*n) + ((9*I)/2)/(b^2*d^2*n^2*Pi))*x^3*Erf[((1/2 + I/2)*(3/n + I*a*b*d^2*Pi + I*b^2*d^2*Pi*Log[c*x^n]))/(b*d*Sqrt[Pi])])/(c*x^n)^(3/n) + ((1/12 - I/12)*E^((-3*a)/(b*n) - ((9*I)/2)/(b^2*d^2*n^2*Pi))*x^3*Erfi[((1/2 + I/2)*(3/n - I*a*b*d^2*Pi - I*b^2*d^2*Pi*Log[c*x^n]))/(b*d*Sqrt[Pi])])/(c*x^n)^(3/n) + (x^3*FresnelS[d*(a + b*Log[c*x^n])])/3","A",14,9,17,0.5294,1,"{6471, 4617, 2278, 2274, 15, 2276, 2234, 2204, 2205}"
55,1,227,0,0.4352353,"\int x S\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[x*FresnelS[d*(a + b*Log[c*x^n])],x]","\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)","\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,"((1/8 - I/8)*E^((2*I - 2*a*b*d^2*n*Pi)/(b^2*d^2*n^2*Pi))*x^2*Erf[((1/2 + I/2)*(2/n + I*a*b*d^2*Pi + I*b^2*d^2*Pi*Log[c*x^n]))/(b*d*Sqrt[Pi])])/(c*x^n)^(2/n) + ((1/8 - I/8)*x^2*Erfi[((1/2 + I/2)*(2/n - I*a*b*d^2*Pi - I*b^2*d^2*Pi*Log[c*x^n]))/(b*d*Sqrt[Pi])])/(E^((2*(I + a*b*d^2*n*Pi))/(b^2*d^2*n^2*Pi))*(c*x^n)^(2/n)) + (x^2*FresnelS[d*(a + b*Log[c*x^n])])/2","A",14,9,15,0.6000,1,"{6471, 4617, 2278, 2274, 15, 2276, 2234, 2204, 2205}"
56,1,214,0,0.326252,"\int S\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[FresnelS[d*(a + b*Log[c*x^n])],x]","\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)","\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,"((1/4 - I/4)*x*Erf[((1/2 + I/2)*(n^(-1) + I*a*b*d^2*Pi + I*b^2*d^2*Pi*Log[c*x^n]))/(b*d*Sqrt[Pi])])/(E^((2*a*b*n - I/(d^2*Pi))/(2*b^2*n^2))*(c*x^n)^n^(-1)) + ((1/4 - I/4)*x*Erfi[((1/2 + I/2)*(n^(-1) - I*a*b*d^2*Pi - I*b^2*d^2*Pi*Log[c*x^n]))/(b*d*Sqrt[Pi])])/(E^((2*a*b*n + I/(d^2*Pi))/(2*b^2*n^2))*(c*x^n)^n^(-1)) + x*FresnelS[d*(a + b*Log[c*x^n])]","A",14,9,13,0.6923,1,"{6468, 4615, 2277, 2274, 15, 2276, 2234, 2204, 2205}"
57,1,65,0,0.0411381,"\int \frac{S\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x} \, dx","Int[FresnelS[d*(a + b*Log[c*x^n])]/x,x]","\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}","\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[(d^2*Pi*(a + b*Log[c*x^n])^2)/2]/(b*d*n*Pi) + (FresnelS[d*(a + b*Log[c*x^n])]*(a + b*Log[c*x^n]))/(b*n)","A",3,1,17,0.05882,1,"{6418}"
58,1,217,0,0.5111875,"\int \frac{S\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^2} \, dx","Int[FresnelS[d*(a + b*Log[c*x^n])]/x^2,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}","\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 - I/4)*E^((2*a*b*n + I/(d^2*Pi))/(2*b^2*n^2))*(c*x^n)^n^(-1)*Erf[((1/2 + I/2)*(n^(-1) - I*a*b*d^2*Pi - I*b^2*d^2*Pi*Log[c*x^n]))/(b*d*Sqrt[Pi])])/x + ((1/4 - I/4)*E^((2*a*b*n - I/(d^2*Pi))/(2*b^2*n^2))*(c*x^n)^n^(-1)*Erfi[((1/2 + I/2)*(n^(-1) + I*a*b*d^2*Pi + I*b^2*d^2*Pi*Log[c*x^n]))/(b*d*Sqrt[Pi])])/x - FresnelS[d*(a + b*Log[c*x^n])]/x","A",14,9,17,0.5294,1,"{6471, 4617, 2278, 2274, 15, 2276, 2234, 2204, 2205}"
59,1,228,0,0.523086,"\int \frac{S\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^3} \, dx","Int[FresnelS[d*(a + b*Log[c*x^n])]/x^3,x]","\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}","\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,"((1/8 - I/8)*E^((2*I + 2*a*b*d^2*n*Pi)/(b^2*d^2*n^2*Pi))*(c*x^n)^(2/n)*Erf[((1/2 + I/2)*(2/n - I*a*b*d^2*Pi - I*b^2*d^2*Pi*Log[c*x^n]))/(b*d*Sqrt[Pi])])/x^2 + ((1/8 - I/8)*(c*x^n)^(2/n)*Erfi[((1/2 + I/2)*(2/n + I*a*b*d^2*Pi + I*b^2*d^2*Pi*Log[c*x^n]))/(b*d*Sqrt[Pi])])/(E^((2*(I - a*b*d^2*n*Pi))/(b^2*d^2*n^2*Pi))*x^2) - FresnelS[d*(a + b*Log[c*x^n])]/(2*x^2)","A",14,9,17,0.5294,1,"{6471, 4617, 2278, 2274, 15, 2276, 2234, 2204, 2205}"
60,1,280,0,0.701812,"\int (e x)^m S\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[(e*x)^m*FresnelS[d*(a + b*Log[c*x^n])],x]","\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)}","\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,"((1/4 - I/4)*E^(((I/2)*(1 + m)*(1 + m + (2*I)*a*b*d^2*n*Pi))/(b^2*d^2*n^2*Pi))*x*(e*x)^m*Erf[((1/2 + I/2)*(1 + m + I*a*b*d^2*n*Pi + I*b^2*d^2*n*Pi*Log[c*x^n]))/(b*d*n*Sqrt[Pi])])/((1 + m)*(c*x^n)^((1 + m)/n)) + ((1/4 - I/4)*x*(e*x)^m*Erfi[((1/2 + I/2)*(1 + m - I*a*b*d^2*n*Pi - I*b^2*d^2*n*Pi*Log[c*x^n]))/(b*d*n*Sqrt[Pi])])/(E^(((I/2)*(1 + m)*(1 + m - (2*I)*a*b*d^2*n*Pi))/(b^2*d^2*n^2*Pi))*(1 + m)*(c*x^n)^((1 + m)/n)) + ((e*x)^(1 + m)*FresnelS[d*(a + b*Log[c*x^n])])/(e*(1 + m))","A",16,10,19,0.5263,1,"{6471, 4617, 2278, 2274, 15, 20, 2276, 2234, 2204, 2205}"
61,1,64,0,0.0692265,"\int e^{c+\frac{1}{2} i b^2 \pi  x^2} S(b x) \, dx","Int[E^(c + (I/2)*b^2*Pi*x^2)*FresnelS[b*x],x]","\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}","\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,"-(E^c*Erfi[(1/2 + I/2)*b*Sqrt[Pi]*x]^2)/(8*b) + (I/4)*b*E^c*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (I/2)*b^2*Pi*x^2]","A",4,4,22,0.1818,1,"{6436, 6376, 6375, 30}"
62,1,64,0,0.0681901,"\int e^{c-\frac{1}{2} i b^2 \pi  x^2} S(b x) \, dx","Int[E^(c - (I/2)*b^2*Pi*x^2)*FresnelS[b*x],x]","\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)","\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,"(E^c*Erf[(1/2 + I/2)*b*Sqrt[Pi]*x]^2)/(8*b) - (I/4)*b*E^c*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (-I/2)*b^2*Pi*x^2]","A",4,4,22,0.1818,1,"{6436, 6373, 30, 6378}"
63,1,101,0,0.0566188,"\int S(b x) \sin \left(c+\frac{1}{2} b^2 \pi  x^2\right) \, dx","Int[FresnelS[b*x]*Sin[c + (b^2*Pi*x^2)/2],x]","-\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) \text{FresnelC}(b x) S(b x)}{2 b}+\frac{\cos (c) S(b x)^2}{2 b}","-\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) \text{FresnelC}(b x) S(b x)}{2 b}+\frac{\cos (c) S(b x)^2}{2 b}",1,"(Cos[c]*FresnelS[b*x]^2)/(2*b) + (FresnelC[b*x]*FresnelS[b*x]*Sin[c])/(2*b) - (I/8)*b*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (-I/2)*b^2*Pi*x^2]*Sin[c] + (I/8)*b*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (I/2)*b^2*Pi*x^2]*Sin[c]","A",4,4,19,0.2105,1,"{6442, 6446, 6440, 30}"
64,1,101,0,0.049668,"\int \cos \left(c+\frac{1}{2} b^2 \pi  x^2\right) S(b x) \, dx","Int[Cos[c + (b^2*Pi*x^2)/2]*FresnelS[b*x],x]","-\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) \text{FresnelC}(b x) S(b x)}{2 b}-\frac{\sin (c) S(b x)^2}{2 b}","-\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) \text{FresnelC}(b x) S(b x)}{2 b}-\frac{\sin (c) S(b x)^2}{2 b}",1,"(Cos[c]*FresnelC[b*x]*FresnelS[b*x])/(2*b) - (I/8)*b*x^2*Cos[c]*HypergeometricPFQ[{1, 1}, {3/2, 2}, (-I/2)*b^2*Pi*x^2] + (I/8)*b*x^2*Cos[c]*HypergeometricPFQ[{1, 1}, {3/2, 2}, (I/2)*b^2*Pi*x^2] - (FresnelS[b*x]^2*Sin[c])/(2*b)","A",4,4,19,0.2105,1,"{6448, 6446, 6440, 30}"
65,1,13,0,0.0147598,"\int S(b x)^2 \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Int[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",2,2,19,0.1053,1,"{6440, 30}"
66,1,13,0,0.0113005,"\int S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Int[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",2,2,17,0.1176,1,"{6440, 30}"
67,1,9,0,0.0147908,"\int \frac{\sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{S(b x)} \, dx","Int[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",2,2,19,0.1053,1,"{6440, 29}"
68,1,11,0,0.0148235,"\int \frac{\sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{S(b x)^2} \, dx","Int[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",2,2,19,0.1053,1,"{6440, 30}"
69,1,13,0,0.0149547,"\int \frac{\sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{S(b x)^3} \, dx","Int[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*b*FresnelS[b*x]^2)","A",2,2,19,0.1053,1,"{6440, 30}"
70,1,17,0,0.0176465,"\int S(b x)^n \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Int[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",2,2,19,0.1053,1,"{6440, 30}"
71,1,232,0,0.3841081,"\int x^8 S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Int[x^8*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2],x]","\frac{7 x^5 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{105 x S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^4 b^8}-\frac{x^7 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{35 x^3 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}+\frac{105 S(b x)^2}{2 \pi ^4 b^9}-\frac{7 x^6}{12 \pi ^2 b^3}+\frac{105 x^2}{4 \pi ^4 b^7}+\frac{5 x^4 \sin \left(\pi  b^2 x^2\right)}{2 \pi ^3 b^5}-\frac{40 \sin \left(\pi  b^2 x^2\right)}{\pi ^5 b^9}-\frac{x^6 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}+\frac{55 x^2 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^4 b^7}","\frac{7 x^5 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{105 x S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^4 b^8}-\frac{x^7 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{35 x^3 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}+\frac{105 S(b x)^2}{2 \pi ^4 b^9}-\frac{7 x^6}{12 \pi ^2 b^3}+\frac{105 x^2}{4 \pi ^4 b^7}+\frac{5 x^4 \sin \left(\pi  b^2 x^2\right)}{2 \pi ^3 b^5}-\frac{40 \sin \left(\pi  b^2 x^2\right)}{\pi ^5 b^9}-\frac{x^6 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}+\frac{55 x^2 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^4 b^7}",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",22,9,20,0.4500,1,"{6454, 6462, 3379, 3309, 30, 3296, 2637, 2634, 6440}"
72,1,216,0,0.264901,"\int x^7 S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Int[x^7*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2],x]","-\frac{531 \text{FresnelC}\left(\sqrt{2} b x\right)}{16 \sqrt{2} \pi ^4 b^8}+\frac{6 x^4 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{48 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^4 b^8}-\frac{x^6 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{24 x^2 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}-\frac{3 x^5}{5 \pi ^2 b^3}+\frac{17 x^3 \sin \left(\pi  b^2 x^2\right)}{8 \pi ^3 b^5}-\frac{x^5 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}+\frac{147 x \cos \left(\pi  b^2 x^2\right)}{16 \pi ^4 b^7}+\frac{24 x}{\pi ^4 b^7}","-\frac{531 \text{FresnelC}\left(\sqrt{2} b x\right)}{16 \sqrt{2} \pi ^4 b^8}+\frac{6 x^4 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{48 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^4 b^8}-\frac{x^6 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{24 x^2 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}-\frac{3 x^5}{5 \pi ^2 b^3}+\frac{17 x^3 \sin \left(\pi  b^2 x^2\right)}{8 \pi ^3 b^5}-\frac{x^5 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}+\frac{147 x \cos \left(\pi  b^2 x^2\right)}{16 \pi ^4 b^7}+\frac{24 x}{\pi ^4 b^7}",1,"(24*x)/(b^7*Pi^4) - (3*x^5)/(5*b^3*Pi^2) + (147*x*Cos[b^2*Pi*x^2])/(16*b^7*Pi^4) - (x^5*Cos[b^2*Pi*x^2])/(4*b^3*Pi^2) - (531*FresnelC[Sqrt[2]*b*x])/(16*Sqrt[2]*b^8*Pi^4) + (24*x^2*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(b^6*Pi^3) - (x^6*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(b^2*Pi) - (48*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^8*Pi^4) + (6*x^4*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^4*Pi^2) + (17*x^3*Sin[b^2*Pi*x^2])/(8*b^5*Pi^3)","A",18,9,20,0.4500,1,"{6454, 6462, 3391, 30, 3386, 3385, 3352, 6460, 3357}"
73,1,248,0,0.2546428,"\int x^6 S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Int[x^6*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2],x]","\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 \text{FresnelC}(b x) S(b x)}{2 \pi ^3 b^7}+\frac{5 x^3 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{x^5 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{15 x S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}-\frac{5 x^4}{8 \pi ^2 b^3}+\frac{7 x^2 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^3 b^5}-\frac{x^4 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}+\frac{11 \cos \left(\pi  b^2 x^2\right)}{2 \pi ^4 b^7}","\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 \text{FresnelC}(b x) S(b x)}{2 \pi ^3 b^7}+\frac{5 x^3 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{x^5 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{15 x S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}-\frac{5 x^4}{8 \pi ^2 b^3}+\frac{7 x^2 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^3 b^5}-\frac{x^4 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}+\frac{11 \cos \left(\pi  b^2 x^2\right)}{2 \pi ^4 b^7}",1,"(-5*x^4)/(8*b^3*Pi^2) + (11*Cos[b^2*Pi*x^2])/(2*b^7*Pi^4) - (x^4*Cos[b^2*Pi*x^2])/(4*b^3*Pi^2) + (15*x*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(b^6*Pi^3) - (x^5*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(b^2*Pi) - (15*FresnelC[b*x]*FresnelS[b*x])/(2*b^7*Pi^3) + (((15*I)/8)*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (-I/2)*b^2*Pi*x^2])/(b^5*Pi^3) - (((15*I)/8)*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (I/2)*b^2*Pi*x^2])/(b^5*Pi^3) + (5*x^3*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^4*Pi^2) + (7*x^2*Sin[b^2*Pi*x^2])/(4*b^5*Pi^3)","A",15,8,20,0.4000,1,"{6454, 6462, 3379, 3309, 30, 3296, 2638, 6446}"
74,1,158,0,0.156292,"\int x^5 S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Int[x^5*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2],x]","\frac{4 x^2 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\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{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{11 x \sin \left(\pi  b^2 x^2\right)}{8 \pi ^3 b^5}-\frac{x^3 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}","\frac{4 x^2 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\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{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{11 x \sin \left(\pi  b^2 x^2\right)}{8 \pi ^3 b^5}-\frac{x^3 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}",1,"(-2*x^3)/(3*b^3*Pi^2) - (x^3*Cos[b^2*Pi*x^2])/(4*b^3*Pi^2) + (8*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(b^6*Pi^3) - (x^4*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(b^2*Pi) - (43*FresnelS[Sqrt[2]*b*x])/(8*Sqrt[2]*b^6*Pi^3) + (4*x^2*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^4*Pi^2) + (11*x*Sin[b^2*Pi*x^2])/(8*b^5*Pi^3)","A",11,8,20,0.4000,1,"{6454, 6462, 3391, 30, 3386, 3351, 6452, 3385}"
75,1,120,0,0.1184058,"\int x^4 S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Int[x^4*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2],x]","\frac{3 x S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{x^3 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{3 S(b x)^2}{2 \pi ^2 b^5}-\frac{3 x^2}{4 \pi ^2 b^3}+\frac{\sin \left(\pi  b^2 x^2\right)}{\pi ^3 b^5}-\frac{x^2 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}","\frac{3 x S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{x^3 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{3 S(b x)^2}{2 \pi ^2 b^5}-\frac{3 x^2}{4 \pi ^2 b^3}+\frac{\sin \left(\pi  b^2 x^2\right)}{\pi ^3 b^5}-\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",9,8,20,0.4000,1,"{6454, 6462, 3379, 2634, 6440, 30, 3296, 2637}"
76,1,105,0,0.081234,"\int x^3 S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Int[x^3*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2],x]","\frac{5 \text{FresnelC}\left(\sqrt{2} b x\right)}{4 \sqrt{2} \pi ^2 b^4}+\frac{2 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{x^2 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{x \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}-\frac{x}{\pi ^2 b^3}","\frac{5 \text{FresnelC}\left(\sqrt{2} b x\right)}{4 \sqrt{2} \pi ^2 b^4}+\frac{2 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{x^2 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{x \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}-\frac{x}{\pi ^2 b^3}",1,"-(x/(b^3*Pi^2)) - (x*Cos[b^2*Pi*x^2])/(4*b^3*Pi^2) + (5*FresnelC[Sqrt[2]*b*x])/(4*Sqrt[2]*b^4*Pi^2) - (x^2*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(b^2*Pi) + (2*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^4*Pi^2)","A",7,5,20,0.2500,1,"{6454, 6460, 3357, 3352, 3385}"
77,1,137,0,0.0606421,"\int x^2 S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Int[x^2*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2],x]","-\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{\text{FresnelC}(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}","-\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{\text{FresnelC}(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,"-Cos[b^2*Pi*x^2]/(4*b^3*Pi^2) - (x*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(b^2*Pi) + (FresnelC[b*x]*FresnelS[b*x])/(2*b^3*Pi) - ((I/8)*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (-I/2)*b^2*Pi*x^2])/(b*Pi) + ((I/8)*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (I/2)*b^2*Pi*x^2])/(b*Pi)","A",4,4,20,0.2000,1,"{6454, 6446, 3379, 2638}"
78,1,49,0,0.0216188,"\int x S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Int[x*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2],x]","\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}","\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,"-((Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(b^2*Pi)) + FresnelS[Sqrt[2]*b*x]/(2*Sqrt[2]*b^2*Pi)","A",2,2,18,0.1111,1,"{6452, 3351}"
79,1,13,0,0.0114849,"\int S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Int[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",2,2,17,0.1176,1,"{6440, 30}"
80,0,0,0,0.0183464,"\int \frac{S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x} \, dx","Int[(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,"Defer[Int][(FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/x, x]","A",0,0,0,0,-1,"{}"
81,0,0,0,0.0184603,"\int \frac{S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^2} \, dx","Int[(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,"Defer[Int][(FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/x^2, x]","A",0,0,0,0,-1,"{}"
82,0,0,0,0.0584933,"\int \frac{S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^3} \, dx","Int[(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,"-b/(4*x) + (b*Cos[b^2*Pi*x^2])/(4*x) + (b^2*Pi*FresnelS[Sqrt[2]*b*x])/(2*Sqrt[2]) - (FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(2*x^2) + (b^2*Pi*Defer[Int][(Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/x, x])/2","A",0,0,0,0,-1,"{}"
83,1,109,0,0.1162019,"\int \frac{S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^4} \, dx","Int[(FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/x^4,x]","-\frac{S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 x^3}-\frac{\pi  b^2 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 x}-\frac{1}{6} \pi ^2 b^3 S(b x)^2+\frac{1}{6} \pi  b^3 \text{Si}\left(b^2 \pi  x^2\right)+\frac{b \cos \left(\pi  b^2 x^2\right)}{12 x^2}-\frac{b}{12 x^2}","-\frac{S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 x^3}-\frac{\pi  b^2 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 x}-\frac{1}{6} \pi ^2 b^3 S(b x)^2+\frac{1}{6} \pi  b^3 \text{Si}\left(b^2 \pi  x^2\right)+\frac{b \cos \left(\pi  b^2 x^2\right)}{12 x^2}-\frac{b}{12 x^2}",1,"-b/(12*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",8,8,20,0.4000,1,"{6456, 6464, 6440, 30, 3375, 3380, 3297, 3299}"
84,0,0,0,0.1213314,"\int \frac{S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^5} \, dx","Int[(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 \text{FresnelC}\left(\sqrt{2} b x\right)}{24 \sqrt{2}}-\frac{S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 x^4}-\frac{\pi  b^2 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{8 x^2}-\frac{7 \pi  b^3 \sin \left(\pi  b^2 x^2\right)}{48 x}+\frac{b \cos \left(\pi  b^2 x^2\right)}{24 x^3}-\frac{b}{24 x^3}",0,"-b/(24*x^3) + (b*Cos[b^2*Pi*x^2])/(24*x^3) + (7*b^4*Pi^2*FresnelC[Sqrt[2]*b*x])/(24*Sqrt[2]) - (b^2*Pi*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(8*x^2) - (FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(4*x^4) - (7*b^3*Pi*Sin[b^2*Pi*x^2])/(48*x) - (b^4*Pi^2*Defer[Int][(FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/x, x])/8","A",0,0,0,0,-1,"{}"
85,0,0,0,0.1925405,"\int \frac{S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^6} \, dx","Int[(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{1}{24} \pi ^2 b^5 \text{CosIntegral}\left(\pi  b^2 x^2\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{\pi  b^3 \sin \left(\pi  b^2 x^2\right)}{24 x^2}+\frac{b \cos \left(\pi  b^2 x^2\right)}{40 x^4}-\frac{b}{40 x^4}",0,"-b/(40*x^4) + (b*Cos[b^2*Pi*x^2])/(40*x^4) + (b^5*Pi^2*CosIntegral[b^2*Pi*x^2])/24 - (b^2*Pi*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(15*x^3) - (FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(5*x^5) - (b^3*Pi*Sin[b^2*Pi*x^2])/(24*x^2) - (b^4*Pi^2*Defer[Int][(FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/x^2, x])/15","A",0,0,0,0,-1,"{}"
86,0,0,0,0.2067179,"\int \frac{S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^7} \, dx","Int[(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{\pi ^2 b^4 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{48 x^2}-\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{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{13 \pi  b^3 \sin \left(\pi  b^2 x^2\right)}{720 x^3}-\frac{67 \pi ^2 b^5 \cos \left(\pi  b^2 x^2\right)}{1440 x}+\frac{b \cos \left(\pi  b^2 x^2\right)}{60 x^5}+\frac{\pi ^2 b^5}{96 x}-\frac{b}{60 x^5}",0,"-b/(60*x^5) + (b^5*Pi^2)/(96*x) + (b*Cos[b^2*Pi*x^2])/(60*x^5) - (67*b^5*Pi^2*Cos[b^2*Pi*x^2])/(1440*x) - (b^2*Pi*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(24*x^4) - (7*b^6*Pi^3*FresnelS[Sqrt[2]*b*x])/(144*Sqrt[2]) - (Sqrt[2]*b^6*Pi^3*FresnelS[Sqrt[2]*b*x])/45 - (FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(6*x^6) + (b^4*Pi^2*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(48*x^2) - (13*b^3*Pi*Sin[b^2*Pi*x^2])/(720*x^3) - (b^6*Pi^3*Defer[Int][(Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/x, x])/48","A",0,0,0,0,-1,"{}"
87,1,224,0,0.3534887,"\int \frac{S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^8} \, dx","Int[(FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/x^8,x]","\frac{\pi ^2 b^4 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{105 x^3}-\frac{S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 x^7}+\frac{\pi ^3 b^6 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{105 x}-\frac{\pi  b^2 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{35 x^5}+\frac{1}{210} \pi ^4 b^7 S(b x)^2-\frac{1}{70} \pi ^3 b^7 \text{Si}\left(b^2 \pi  x^2\right)+\frac{\pi ^2 b^5}{420 x^2}-\frac{\pi  b^3 \sin \left(\pi  b^2 x^2\right)}{105 x^4}-\frac{\pi ^2 b^5 \cos \left(\pi  b^2 x^2\right)}{84 x^2}+\frac{b \cos \left(\pi  b^2 x^2\right)}{84 x^6}-\frac{b}{84 x^6}","\frac{\pi ^2 b^4 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{105 x^3}-\frac{S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 x^7}+\frac{\pi ^3 b^6 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{105 x}-\frac{\pi  b^2 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{35 x^5}+\frac{1}{210} \pi ^4 b^7 S(b x)^2-\frac{1}{70} \pi ^3 b^7 \text{Si}\left(b^2 \pi  x^2\right)+\frac{\pi ^2 b^5}{420 x^2}-\frac{\pi  b^3 \sin \left(\pi  b^2 x^2\right)}{105 x^4}-\frac{\pi ^2 b^5 \cos \left(\pi  b^2 x^2\right)}{84 x^2}+\frac{b \cos \left(\pi  b^2 x^2\right)}{84 x^6}-\frac{b}{84 x^6}",1,"-b/(84*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",19,9,20,0.4500,1,"{6456, 6464, 6440, 30, 3375, 3380, 3297, 3299, 3379}"
88,0,0,0,0.3062472,"\int \frac{S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^9} \, dx","Int[(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 \text{FresnelC}\left(\sqrt{2} b x\right)}{40320 \sqrt{2}}+\frac{\pi ^2 b^4 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{192 x^4}-\frac{S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{8 x^8}+\frac{\pi ^3 b^6 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{384 x^2}-\frac{\pi  b^2 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{48 x^6}+\frac{\pi ^2 b^5}{1152 x^3}+\frac{853 \pi ^3 b^7 \sin \left(\pi  b^2 x^2\right)}{80640 x}-\frac{19 \pi  b^3 \sin \left(\pi  b^2 x^2\right)}{3360 x^5}-\frac{187 \pi ^2 b^5 \cos \left(\pi  b^2 x^2\right)}{40320 x^3}+\frac{b \cos \left(\pi  b^2 x^2\right)}{112 x^7}-\frac{b}{112 x^7}",0,"-b/(112*x^7) + (b^5*Pi^2)/(1152*x^3) + (b*Cos[b^2*Pi*x^2])/(112*x^7) - (187*b^5*Pi^2*Cos[b^2*Pi*x^2])/(40320*x^3) - (853*b^8*Pi^4*FresnelC[Sqrt[2]*b*x])/(40320*Sqrt[2]) - (b^2*Pi*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(48*x^6) + (b^6*Pi^3*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(384*x^2) - (FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(8*x^8) + (b^4*Pi^2*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(192*x^4) - (19*b^3*Pi*Sin[b^2*Pi*x^2])/(3360*x^5) + (853*b^7*Pi^3*Sin[b^2*Pi*x^2])/(80640*x) + (b^8*Pi^4*Defer[Int][(FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/x, x])/384","A",0,0,0,0,-1,"{}"
89,0,0,0,0.4768232,"\int \frac{S(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^{10}} \, dx","Int[(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{5 \pi ^4 b^9 \text{CosIntegral}\left(\pi  b^2 x^2\right)}{2016}+\frac{\pi ^2 b^4 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{315 x^5}-\frac{S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{9 x^9}+\frac{\pi ^3 b^6 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{945 x^3}-\frac{\pi  b^2 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{63 x^7}+\frac{\pi ^2 b^5}{2520 x^4}+\frac{5 \pi ^3 b^7 \sin \left(\pi  b^2 x^2\right)}{2016 x^2}-\frac{11 \pi  b^3 \sin \left(\pi  b^2 x^2\right)}{3024 x^6}-\frac{67 \pi ^2 b^5 \cos \left(\pi  b^2 x^2\right)}{30240 x^4}+\frac{b \cos \left(\pi  b^2 x^2\right)}{144 x^8}-\frac{b}{144 x^8}",0,"-b/(144*x^8) + (b^5*Pi^2)/(2520*x^4) + (b*Cos[b^2*Pi*x^2])/(144*x^8) - (67*b^5*Pi^2*Cos[b^2*Pi*x^2])/(30240*x^4) - (5*b^9*Pi^4*CosIntegral[b^2*Pi*x^2])/2016 - (b^2*Pi*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(63*x^7) + (b^6*Pi^3*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(945*x^3) - (FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(9*x^9) + (b^4*Pi^2*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(315*x^5) - (11*b^3*Pi*Sin[b^2*Pi*x^2])/(3024*x^6) + (5*b^7*Pi^3*Sin[b^2*Pi*x^2])/(2016*x^2) + (b^8*Pi^4*Defer[Int][(FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/x^2, x])/945","A",0,0,0,0,-1,"{}"
90,0,0,0,0.0146736,"\int \cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x)^n \, dx","Int[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,"Defer[Int][Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x]^n, x]","A",0,0,0,0,-1,"{}"
91,1,307,0,0.4416209,"\int x^8 \cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x) \, dx","Int[x^8*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x],x]","-\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 \text{FresnelC}(b x) S(b x)}{2 \pi ^4 b^9}+\frac{x^7 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{35 x^3 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}+\frac{7 x^5 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{105 x S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^4 b^8}+\frac{35 x^4}{8 \pi ^3 b^5}+\frac{x^6 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}-\frac{55 x^2 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^4 b^7}+\frac{5 x^4 \cos \left(\pi  b^2 x^2\right)}{2 \pi ^3 b^5}-\frac{40 \cos \left(\pi  b^2 x^2\right)}{\pi ^5 b^9}-\frac{x^8}{16 \pi  b}","-\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 \text{FresnelC}(b x) S(b x)}{2 \pi ^4 b^9}+\frac{x^7 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{35 x^3 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}+\frac{7 x^5 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{105 x S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^4 b^8}+\frac{35 x^4}{8 \pi ^3 b^5}+\frac{x^6 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}-\frac{55 x^2 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^4 b^7}+\frac{5 x^4 \cos \left(\pi  b^2 x^2\right)}{2 \pi ^3 b^5}-\frac{40 \cos \left(\pi  b^2 x^2\right)}{\pi ^5 b^9}-\frac{x^8}{16 \pi  b}",1,"(35*x^4)/(8*b^5*Pi^3) - x^8/(16*b*Pi) - (40*Cos[b^2*Pi*x^2])/(b^9*Pi^5) + (5*x^4*Cos[b^2*Pi*x^2])/(2*b^5*Pi^3) - (105*x*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(b^8*Pi^4) + (7*x^5*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(b^4*Pi^2) + (105*FresnelC[b*x]*FresnelS[b*x])/(2*b^9*Pi^4) - (((105*I)/8)*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (-I/2)*b^2*Pi*x^2])/(b^7*Pi^4) + (((105*I)/8)*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (I/2)*b^2*Pi*x^2])/(b^7*Pi^4) - (35*x^3*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^6*Pi^3) + (x^7*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^2*Pi) - (55*x^2*Sin[b^2*Pi*x^2])/(4*b^7*Pi^4) + (x^6*Sin[b^2*Pi*x^2])/(4*b^3*Pi^2)","A",23,8,20,0.4000,1,"{6462, 3379, 3309, 30, 3296, 2638, 6454, 6446}"
92,1,217,0,0.2714287,"\int x^7 \cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x) \, dx","Int[x^7*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x],x]","\frac{x^6 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{24 x^2 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}+\frac{6 x^4 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{48 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\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^5 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}-\frac{147 x \sin \left(\pi  b^2 x^2\right)}{16 \pi ^4 b^7}+\frac{17 x^3 \cos \left(\pi  b^2 x^2\right)}{8 \pi ^3 b^5}-\frac{x^7}{14 \pi  b}","\frac{x^6 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{24 x^2 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}+\frac{6 x^4 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{48 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\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^5 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}-\frac{147 x \sin \left(\pi  b^2 x^2\right)}{16 \pi ^4 b^7}+\frac{17 x^3 \cos \left(\pi  b^2 x^2\right)}{8 \pi ^3 b^5}-\frac{x^7}{14 \pi  b}",1,"(4*x^3)/(b^5*Pi^3) - x^7/(14*b*Pi) + (17*x^3*Cos[b^2*Pi*x^2])/(8*b^5*Pi^3) - (48*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(b^8*Pi^4) + (6*x^4*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(b^4*Pi^2) + (531*FresnelS[Sqrt[2]*b*x])/(16*Sqrt[2]*b^8*Pi^4) - (24*x^2*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^6*Pi^3) + (x^6*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^2*Pi) - (147*x*Sin[b^2*Pi*x^2])/(16*b^7*Pi^4) + (x^5*Sin[b^2*Pi*x^2])/(4*b^3*Pi^2)","A",18,8,20,0.4000,1,"{6462, 3391, 30, 3386, 3385, 3351, 6454, 6452}"
93,1,184,0,0.253349,"\int x^6 \cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x) \, dx","Int[x^6*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x],x]","\frac{x^5 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{15 x S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}+\frac{5 x^3 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}+\frac{15 S(b x)^2}{2 \pi ^3 b^7}+\frac{15 x^2}{4 \pi ^3 b^5}+\frac{x^4 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}-\frac{11 \sin \left(\pi  b^2 x^2\right)}{2 \pi ^4 b^7}+\frac{7 x^2 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^3 b^5}-\frac{x^6}{12 \pi  b}","\frac{x^5 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{15 x S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}+\frac{5 x^3 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}+\frac{15 S(b x)^2}{2 \pi ^3 b^7}+\frac{15 x^2}{4 \pi ^3 b^5}+\frac{x^4 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}-\frac{11 \sin \left(\pi  b^2 x^2\right)}{2 \pi ^4 b^7}+\frac{7 x^2 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^3 b^5}-\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",16,9,20,0.4500,1,"{6462, 3379, 3309, 30, 3296, 2637, 6454, 2634, 6440}"
94,1,166,0,0.1688811,"\int x^5 \cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x) \, dx","Int[x^5*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x],x]","-\frac{43 \text{FresnelC}\left(\sqrt{2} b x\right)}{8 \sqrt{2} \pi ^3 b^6}+\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{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{11 x \cos \left(\pi  b^2 x^2\right)}{8 \pi ^3 b^5}+\frac{4 x}{\pi ^3 b^5}-\frac{x^5}{10 \pi  b}","-\frac{43 \text{FresnelC}\left(\sqrt{2} b x\right)}{8 \sqrt{2} \pi ^3 b^6}+\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{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{11 x \cos \left(\pi  b^2 x^2\right)}{8 \pi ^3 b^5}+\frac{4 x}{\pi ^3 b^5}-\frac{x^5}{10 \pi  b}",1,"(4*x)/(b^5*Pi^3) - x^5/(10*b*Pi) + (11*x*Cos[b^2*Pi*x^2])/(8*b^5*Pi^3) - (43*FresnelC[Sqrt[2]*b*x])/(8*Sqrt[2]*b^6*Pi^3) + (4*x^2*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(b^4*Pi^2) - (8*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^6*Pi^3) + (x^4*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^2*Pi) + (x^3*Sin[b^2*Pi*x^2])/(4*b^3*Pi^2)","A",13,9,20,0.4500,1,"{6462, 3391, 30, 3386, 3385, 3352, 6454, 6460, 3357}"
95,1,195,0,0.1573239,"\int x^4 \cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x) \, dx","Int[x^4*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x],x]","\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 \text{FresnelC}(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{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{\cos \left(\pi  b^2 x^2\right)}{\pi ^3 b^5}-\frac{x^4}{8 \pi  b}","\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 \text{FresnelC}(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{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{\cos \left(\pi  b^2 x^2\right)}{\pi ^3 b^5}-\frac{x^4}{8 \pi  b}",1,"-x^4/(8*b*Pi) + Cos[b^2*Pi*x^2]/(b^5*Pi^3) + (3*x*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(b^4*Pi^2) - (3*FresnelC[b*x]*FresnelS[b*x])/(2*b^5*Pi^2) + (((3*I)/8)*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (-I/2)*b^2*Pi*x^2])/(b^3*Pi^2) - (((3*I)/8)*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (I/2)*b^2*Pi*x^2])/(b^3*Pi^2) + (x^3*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^2*Pi) + (x^2*Sin[b^2*Pi*x^2])/(4*b^3*Pi^2)","A",10,8,20,0.4000,1,"{6462, 3379, 3309, 30, 3296, 2638, 6454, 6446}"
96,1,108,0,0.0898809,"\int x^3 \cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x) \, dx","Int[x^3*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x],x]","\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{5 S\left(\sqrt{2} b x\right)}{4 \sqrt{2} \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}","\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{5 S\left(\sqrt{2} b x\right)}{4 \sqrt{2} \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,"-x^3/(6*b*Pi) + (2*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(b^4*Pi^2) - (5*FresnelS[Sqrt[2]*b*x])/(4*Sqrt[2]*b^4*Pi^2) + (x^2*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^2*Pi) + (x*Sin[b^2*Pi*x^2])/(4*b^3*Pi^2)","A",7,6,20,0.3000,1,"{6462, 3391, 30, 3386, 3351, 6452}"
97,1,73,0,0.0547892,"\int x^2 \cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x) \, dx","Int[x^2*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x],x]","\frac{x S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{S(b x)^2}{2 \pi  b^3}+\frac{\sin \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}-\frac{x^2}{4 \pi  b}","\frac{x S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{S(b x)^2}{2 \pi  b^3}+\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) - 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",5,5,20,0.2500,1,"{6462, 3379, 2634, 6440, 30}"
98,1,59,0,0.0321775,"\int x \cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x) \, dx","Int[x*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x],x]","\frac{\text{FresnelC}\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}","\frac{\text{FresnelC}\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,"-x/(2*b*Pi) + FresnelC[Sqrt[2]*b*x]/(2*Sqrt[2]*b^2*Pi) + (FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^2*Pi)","A",4,3,18,0.1667,1,"{6460, 3357, 3352}"
99,1,80,0,0.0167872,"\int \cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x) \, dx","Int[Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x],x]","-\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{\text{FresnelC}(b x) S(b x)}{2 b}","-\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{\text{FresnelC}(b x) S(b x)}{2 b}",1,"(FresnelC[b*x]*FresnelS[b*x])/(2*b) - (I/8)*b*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (-I/2)*b^2*Pi*x^2] + (I/8)*b*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (I/2)*b^2*Pi*x^2]","A",1,1,17,0.05882,1,"{6446}"
100,0,0,0,0.0178919,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x)}{x} \, dx","Int[(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,"Defer[Int][(Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/x, x]","A",0,0,0,0,-1,"{}"
101,1,48,0,0.0413899,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x)}{x^2} \, dx","Int[(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",4,4,20,0.2000,1,"{6464, 6440, 30, 3375}"
102,0,0,0,0.0588469,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x)}{x^3} \, dx","Int[(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 \text{FresnelC}\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,"(b^2*Pi*FresnelC[Sqrt[2]*b*x])/(2*Sqrt[2]) - (Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(2*x^2) - (b*Sin[b^2*Pi*x^2])/(4*x) - (b^2*Pi*Defer[Int][(FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/x, x])/2","A",0,0,0,0,-1,"{}"
103,0,0,0,0.0878529,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x)}{x^4} \, dx","Int[(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{1}{12} \pi  b^3 \text{CosIntegral}\left(\pi  b^2 x^2\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}",0,"(b^3*Pi*CosIntegral[b^2*Pi*x^2])/12 - (Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(3*x^3) - (b*Sin[b^2*Pi*x^2])/(12*x^2) - (b^2*Pi*Defer[Int][(FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/x^2, x])/3","A",0,0,0,0,-1,"{}"
104,0,0,0,0.1262073,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x)}{x^5} \, dx","Int[(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{\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{7 \pi ^2 b^4 S\left(\sqrt{2} b x\right)}{24 \sqrt{2}}-\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}+\frac{\pi  b^3}{16 x}",0,"(b^3*Pi)/(16*x) - (7*b^3*Pi*Cos[b^2*Pi*x^2])/(48*x) - (Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(4*x^4) - (7*b^4*Pi^2*FresnelS[Sqrt[2]*b*x])/(24*Sqrt[2]) + (b^2*Pi*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(8*x^2) - (b*Sin[b^2*Pi*x^2])/(24*x^3) - (b^4*Pi^2*Defer[Int][(Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/x, x])/8","A",0,0,0,0,-1,"{}"
105,1,163,0,0.2136368,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x)}{x^6} \, dx","Int[(Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/x^6,x]","\frac{\pi  b^2 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{15 x^3}+\frac{\pi ^2 b^4 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{15 x}-\frac{S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 x^5}+\frac{1}{30} \pi ^3 b^5 S(b x)^2-\frac{7}{120} \pi ^2 b^5 \text{Si}\left(b^2 \pi  x^2\right)+\frac{\pi  b^3}{60 x^2}-\frac{b \sin \left(\pi  b^2 x^2\right)}{40 x^4}-\frac{\pi  b^3 \cos \left(\pi  b^2 x^2\right)}{24 x^2}","\frac{\pi  b^2 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{15 x^3}+\frac{\pi ^2 b^4 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{15 x}-\frac{S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 x^5}+\frac{1}{30} \pi ^3 b^5 S(b x)^2-\frac{7}{120} \pi ^2 b^5 \text{Si}\left(b^2 \pi  x^2\right)+\frac{\pi  b^3}{60 x^2}-\frac{b \sin \left(\pi  b^2 x^2\right)}{40 x^4}-\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",13,9,20,0.4500,1,"{6464, 6456, 6440, 30, 3375, 3380, 3297, 3299, 3379}"
106,0,0,0,0.2047377,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x)}{x^7} \, dx","Int[(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 \text{FresnelC}\left(\sqrt{2} b x\right)-\frac{7 \pi ^3 b^6 \text{FresnelC}\left(\sqrt{2} b x\right)}{144 \sqrt{2}}+\frac{\pi  b^2 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{24 x^4}+\frac{\pi ^2 b^4 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{48 x^2}-\frac{S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 x^6}+\frac{\pi  b^3}{144 x^3}+\frac{67 \pi ^2 b^5 \sin \left(\pi  b^2 x^2\right)}{1440 x}-\frac{b \sin \left(\pi  b^2 x^2\right)}{60 x^5}-\frac{13 \pi  b^3 \cos \left(\pi  b^2 x^2\right)}{720 x^3}",0,"(b^3*Pi)/(144*x^3) - (13*b^3*Pi*Cos[b^2*Pi*x^2])/(720*x^3) - (7*b^6*Pi^3*FresnelC[Sqrt[2]*b*x])/(144*Sqrt[2]) - (Sqrt[2]*b^6*Pi^3*FresnelC[Sqrt[2]*b*x])/45 - (Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(6*x^6) + (b^4*Pi^2*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(48*x^2) + (b^2*Pi*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(24*x^4) - (b*Sin[b^2*Pi*x^2])/(60*x^5) + (67*b^5*Pi^2*Sin[b^2*Pi*x^2])/(1440*x) + (b^6*Pi^3*Defer[Int][(FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/x, x])/48","A",0,0,0,0,-1,"{}"
107,0,0,0,0.3194272,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x)}{x^8} \, dx","Int[(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{1}{84} \pi ^3 b^7 \text{CosIntegral}\left(\pi  b^2 x^2\right)+\frac{\pi  b^2 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{35 x^5}+\frac{\pi ^2 b^4 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{105 x^3}-\frac{S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 x^7}+\frac{\pi  b^3}{280 x^4}+\frac{\pi ^2 b^5 \sin \left(\pi  b^2 x^2\right)}{84 x^2}-\frac{b \sin \left(\pi  b^2 x^2\right)}{84 x^6}-\frac{\pi  b^3 \cos \left(\pi  b^2 x^2\right)}{105 x^4}",0,"(b^3*Pi)/(280*x^4) - (b^3*Pi*Cos[b^2*Pi*x^2])/(105*x^4) - (b^7*Pi^3*CosIntegral[b^2*Pi*x^2])/84 - (Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(7*x^7) + (b^4*Pi^2*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(105*x^3) + (b^2*Pi*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(35*x^5) - (b*Sin[b^2*Pi*x^2])/(84*x^6) + (b^5*Pi^2*Sin[b^2*Pi*x^2])/(84*x^2) + (b^6*Pi^3*Defer[Int][(FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/x^2, x])/105","A",0,0,0,0,-1,"{}"
108,0,0,0,0.3095261,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x)}{x^9} \, dx","Int[(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{\pi ^3 b^6 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{384 x^2}+\frac{\pi  b^2 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{48 x^6}+\frac{\pi ^2 b^4 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{192 x^4}-\frac{S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{8 x^8}+\frac{853 \pi ^4 b^8 S\left(\sqrt{2} b x\right)}{40320 \sqrt{2}}+\frac{\pi  b^3}{480 x^5}+\frac{187 \pi ^2 b^5 \sin \left(\pi  b^2 x^2\right)}{40320 x^3}-\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{19 \pi  b^3 \cos \left(\pi  b^2 x^2\right)}{3360 x^5}-\frac{\pi ^3 b^7}{768 x}",0,"(b^3*Pi)/(480*x^5) - (b^7*Pi^3)/(768*x) - (19*b^3*Pi*Cos[b^2*Pi*x^2])/(3360*x^5) + (853*b^7*Pi^3*Cos[b^2*Pi*x^2])/(80640*x) - (Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(8*x^8) + (b^4*Pi^2*Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/(192*x^4) + (853*b^8*Pi^4*FresnelS[Sqrt[2]*b*x])/(40320*Sqrt[2]) + (b^2*Pi*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(48*x^6) - (b^6*Pi^3*FresnelS[b*x]*Sin[(b^2*Pi*x^2)/2])/(384*x^2) - (b*Sin[b^2*Pi*x^2])/(112*x^7) + (187*b^5*Pi^2*Sin[b^2*Pi*x^2])/(40320*x^3) + (b^8*Pi^4*Defer[Int][(Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/x, x])/384","A",0,0,0,0,-1,"{}"
109,1,278,0,0.5161731,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) S(b x)}{x^{10}} \, dx","Int[(Cos[(b^2*Pi*x^2)/2]*FresnelS[b*x])/x^10,x]","-\frac{\pi ^3 b^6 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{945 x^3}+\frac{\pi  b^2 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{63 x^7}-\frac{\pi ^4 b^8 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{945 x}+\frac{\pi ^2 b^4 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{315 x^5}-\frac{S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{9 x^9}-\frac{\pi ^5 b^9 S(b x)^2}{1890}+\frac{83 \pi ^4 b^9 \text{Si}\left(b^2 \pi  x^2\right)}{30240}-\frac{\pi ^3 b^7}{3780 x^2}+\frac{\pi  b^3}{756 x^6}+\frac{67 \pi ^2 b^5 \sin \left(\pi  b^2 x^2\right)}{30240 x^4}-\frac{b \sin \left(\pi  b^2 x^2\right)}{144 x^8}+\frac{5 \pi ^3 b^7 \cos \left(\pi  b^2 x^2\right)}{2016 x^2}-\frac{11 \pi  b^3 \cos \left(\pi  b^2 x^2\right)}{3024 x^6}","-\frac{\pi ^3 b^6 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{945 x^3}+\frac{\pi  b^2 S(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{63 x^7}-\frac{\pi ^4 b^8 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{945 x}+\frac{\pi ^2 b^4 S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{315 x^5}-\frac{S(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{9 x^9}-\frac{\pi ^5 b^9 S(b x)^2}{1890}+\frac{83 \pi ^4 b^9 \text{Si}\left(b^2 \pi  x^2\right)}{30240}-\frac{\pi ^3 b^7}{3780 x^2}+\frac{\pi  b^3}{756 x^6}+\frac{67 \pi ^2 b^5 \sin \left(\pi  b^2 x^2\right)}{30240 x^4}-\frac{b \sin \left(\pi  b^2 x^2\right)}{144 x^8}+\frac{5 \pi ^3 b^7 \cos \left(\pi  b^2 x^2\right)}{2016 x^2}-\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",26,9,20,0.4500,1,"{6464, 6456, 6440, 30, 3375, 3380, 3297, 3299, 3379}"
110,1,124,0,0.0821382,"\int x^7 \text{FresnelC}(b x) \, dx","Int[x^7*FresnelC[b*x],x]","-\frac{105 \text{FresnelC}(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{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{105 x \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{8 \pi ^4 b^7}+\frac{1}{8} x^8 \text{FresnelC}(b x)","-\frac{105 \text{FresnelC}(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{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{105 x \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{8 \pi ^4 b^7}+\frac{1}{8} x^8 \text{FresnelC}(b x)",1,"(105*x*Cos[(b^2*Pi*x^2)/2])/(8*b^7*Pi^4) - (7*x^5*Cos[(b^2*Pi*x^2)/2])/(8*b^3*Pi^2) - (105*FresnelC[b*x])/(8*b^8*Pi^4) + (x^8*FresnelC[b*x])/8 + (35*x^3*Sin[(b^2*Pi*x^2)/2])/(8*b^5*Pi^3) - (x^7*Sin[(b^2*Pi*x^2)/2])/(8*b*Pi)","A",6,4,8,0.5000,1,"{6427, 3386, 3385, 3352}"
111,1,109,0,0.1143253,"\int x^6 \text{FresnelC}(b x) \, dx","Int[x^6*FresnelC[b*x],x]","-\frac{x^6 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi  b}+\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{48 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi ^4 b^7}+\frac{1}{7} x^7 \text{FresnelC}(b x)","-\frac{x^6 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi  b}+\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{48 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi ^4 b^7}+\frac{1}{7} x^7 \text{FresnelC}(b x)",1,"(48*Cos[(b^2*Pi*x^2)/2])/(7*b^7*Pi^4) - (6*x^4*Cos[(b^2*Pi*x^2)/2])/(7*b^3*Pi^2) + (x^7*FresnelC[b*x])/7 + (24*x^2*Sin[(b^2*Pi*x^2)/2])/(7*b^5*Pi^3) - (x^6*Sin[(b^2*Pi*x^2)/2])/(7*b*Pi)","A",6,4,8,0.5000,1,"{6427, 3380, 3296, 2638}"
112,1,99,0,0.0624975,"\int x^5 \text{FresnelC}(b x) \, dx","Int[x^5*FresnelC[b*x],x]","-\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 \text{FresnelC}(b x)","-\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 \text{FresnelC}(b x)",1,"(-5*x^3*Cos[(b^2*Pi*x^2)/2])/(6*b^3*Pi^2) + (x^6*FresnelC[b*x])/6 - (5*FresnelS[b*x])/(2*b^6*Pi^3) + (5*x*Sin[(b^2*Pi*x^2)/2])/(2*b^5*Pi^3) - (x^5*Sin[(b^2*Pi*x^2)/2])/(6*b*Pi)","A",5,4,8,0.5000,1,"{6427, 3386, 3385, 3351}"
113,1,84,0,0.0766497,"\int x^4 \text{FresnelC}(b x) \, dx","Int[x^4*FresnelC[b*x],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 \text{FresnelC}(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 \text{FresnelC}(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*Sin[(b^2*Pi*x^2)/2])/(5*b^5*Pi^3) - (x^4*Sin[(b^2*Pi*x^2)/2])/(5*b*Pi)","A",5,4,8,0.5000,1,"{6427, 3380, 3296, 2637}"
114,1,74,0,0.0429744,"\int x^3 \text{FresnelC}(b x) \, dx","Int[x^3*FresnelC[b*x],x]","\frac{3 \text{FresnelC}(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 \text{FresnelC}(b x)","\frac{3 \text{FresnelC}(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 \text{FresnelC}(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",4,4,8,0.5000,1,"{6427, 3386, 3385, 3352}"
115,1,59,0,0.0543763,"\int x^2 \text{FresnelC}(b x) \, dx","Int[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 \text{FresnelC}(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 \text{FresnelC}(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",4,4,8,0.5000,1,"{6427, 3380, 3296, 2638}"
116,1,49,0,0.0258736,"\int x \text{FresnelC}(b x) \, dx","Int[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 \text{FresnelC}(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 \text{FresnelC}(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",3,3,6,0.5000,1,"{6427, 3386, 3351}"
117,1,27,0,0.0047574,"\int \text{FresnelC}(b x) \, dx","Int[FresnelC[b*x],x]","x \text{FresnelC}(b x)-\frac{\sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b}","x \text{FresnelC}(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",1,1,4,0.2500,1,"{6419}"
118,1,69,0,0.0443547,"\int \frac{\text{FresnelC}(b x)}{x} \, dx","Int[FresnelC[b*x]/x,x]","\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)","\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,"(b*x*HypergeometricPFQ[{1/2, 1/2}, {3/2, 3/2}, (-I/2)*b^2*Pi*x^2])/2 + (b*x*HypergeometricPFQ[{1/2, 1/2}, {3/2, 3/2}, (I/2)*b^2*Pi*x^2])/2","A",3,3,8,0.3750,1,"{6425, 6358, 6360}"
119,1,27,0,0.0212742,"\int \frac{\text{FresnelC}(b x)}{x^2} \, dx","Int[FresnelC[b*x]/x^2,x]","\frac{1}{2} b \text{CosIntegral}\left(\frac{1}{2} \pi  b^2 x^2\right)-\frac{\text{FresnelC}(b x)}{x}","\frac{1}{2} b \text{CosIntegral}\left(\frac{1}{2} \pi  b^2 x^2\right)-\frac{\text{FresnelC}(b x)}{x}",1,"(b*CosIntegral[(b^2*Pi*x^2)/2])/2 - FresnelC[b*x]/x","A",2,2,8,0.2500,1,"{6427, 3376}"
120,1,44,0,0.0285715,"\int \frac{\text{FresnelC}(b x)}{x^3} \, dx","Int[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{\text{FresnelC}(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{\text{FresnelC}(b x)}{2 x^2}",1,"-(b*Cos[(b^2*Pi*x^2)/2])/(2*x) - FresnelC[b*x]/(2*x^2) - (b^2*Pi*FresnelS[b*x])/2","A",3,3,8,0.3750,1,"{6427, 3388, 3351}"
121,1,52,0,0.0636539,"\int \frac{\text{FresnelC}(b x)}{x^4} \, dx","Int[FresnelC[b*x]/x^4,x]","-\frac{1}{12} \pi  b^3 \text{Si}\left(\frac{1}{2} b^2 \pi  x^2\right)-\frac{b \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 x^2}-\frac{\text{FresnelC}(b x)}{3 x^3}","-\frac{1}{12} \pi  b^3 \text{Si}\left(\frac{1}{2} b^2 \pi  x^2\right)-\frac{b \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 x^2}-\frac{\text{FresnelC}(b x)}{3 x^3}",1,"-(b*Cos[(b^2*Pi*x^2)/2])/(6*x^2) - FresnelC[b*x]/(3*x^3) - (b^3*Pi*SinIntegral[(b^2*Pi*x^2)/2])/12","A",4,4,8,0.5000,1,"{6427, 3380, 3297, 3299}"
122,1,69,0,0.0411592,"\int \frac{\text{FresnelC}(b x)}{x^5} \, dx","Int[FresnelC[b*x]/x^5,x]","-\frac{1}{12} \pi ^2 b^4 \text{FresnelC}(b x)+\frac{\pi  b^3 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{12 x}-\frac{b \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{12 x^3}-\frac{\text{FresnelC}(b x)}{4 x^4}","-\frac{1}{12} \pi ^2 b^4 \text{FresnelC}(b x)+\frac{\pi  b^3 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{12 x}-\frac{b \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{12 x^3}-\frac{\text{FresnelC}(b x)}{4 x^4}",1,"-(b*Cos[(b^2*Pi*x^2)/2])/(12*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",4,4,8,0.5000,1,"{6427, 3388, 3387, 3352}"
123,1,77,0,0.0893477,"\int \frac{\text{FresnelC}(b x)}{x^6} \, dx","Int[FresnelC[b*x]/x^6,x]","-\frac{1}{80} \pi ^2 b^5 \text{CosIntegral}\left(\frac{1}{2} \pi  b^2 x^2\right)+\frac{\pi  b^3 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{40 x^2}-\frac{b \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{20 x^4}-\frac{\text{FresnelC}(b x)}{5 x^5}","-\frac{1}{80} \pi ^2 b^5 \text{CosIntegral}\left(\frac{1}{2} \pi  b^2 x^2\right)+\frac{\pi  b^3 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{40 x^2}-\frac{b \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{20 x^4}-\frac{\text{FresnelC}(b x)}{5 x^5}",1,"-(b*Cos[(b^2*Pi*x^2)/2])/(20*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",5,4,8,0.5000,1,"{6427, 3380, 3297, 3302}"
124,1,94,0,0.0587288,"\int \frac{\text{FresnelC}(b x)}{x^7} \, dx","Int[FresnelC[b*x]/x^7,x]","\frac{1}{90} \pi ^3 b^6 S(b x)+\frac{\pi  b^3 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{90 x^3}+\frac{\pi ^2 b^5 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{90 x}-\frac{b \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{30 x^5}-\frac{\text{FresnelC}(b x)}{6 x^6}","\frac{1}{90} \pi ^3 b^6 S(b x)+\frac{\pi  b^3 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{90 x^3}+\frac{\pi ^2 b^5 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{90 x}-\frac{b \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{30 x^5}-\frac{\text{FresnelC}(b x)}{6 x^6}",1,"-(b*Cos[(b^2*Pi*x^2)/2])/(30*x^5) + (b^5*Pi^2*Cos[(b^2*Pi*x^2)/2])/(90*x) - FresnelC[b*x]/(6*x^6) + (b^6*Pi^3*FresnelS[b*x])/90 + (b^3*Pi*Sin[(b^2*Pi*x^2)/2])/(90*x^3)","A",5,4,8,0.5000,1,"{6427, 3388, 3387, 3351}"
125,1,102,0,0.1183971,"\int \frac{\text{FresnelC}(b x)}{x^8} \, dx","Int[FresnelC[b*x]/x^8,x]","\frac{1}{672} \pi ^3 b^7 \text{Si}\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)}{168 x^4}+\frac{\pi ^2 b^5 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{336 x^2}-\frac{b \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{42 x^6}-\frac{\text{FresnelC}(b x)}{7 x^7}","\frac{1}{672} \pi ^3 b^7 \text{Si}\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)}{168 x^4}+\frac{\pi ^2 b^5 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{336 x^2}-\frac{b \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{42 x^6}-\frac{\text{FresnelC}(b x)}{7 x^7}",1,"-(b*Cos[(b^2*Pi*x^2)/2])/(42*x^6) + (b^5*Pi^2*Cos[(b^2*Pi*x^2)/2])/(336*x^2) - FresnelC[b*x]/(7*x^7) + (b^3*Pi*Sin[(b^2*Pi*x^2)/2])/(168*x^4) + (b^7*Pi^3*SinIntegral[(b^2*Pi*x^2)/2])/672","A",6,4,8,0.5000,1,"{6427, 3380, 3297, 3299}"
126,1,119,0,0.0784687,"\int \frac{\text{FresnelC}(b x)}{x^9} \, dx","Int[FresnelC[b*x]/x^9,x]","\frac{1}{840} \pi ^4 b^8 \text{FresnelC}(b x)-\frac{\pi ^3 b^7 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{840 x}+\frac{\pi  b^3 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{280 x^5}+\frac{\pi ^2 b^5 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{840 x^3}-\frac{b \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{56 x^7}-\frac{\text{FresnelC}(b x)}{8 x^8}","\frac{1}{840} \pi ^4 b^8 \text{FresnelC}(b x)-\frac{\pi ^3 b^7 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{840 x}+\frac{\pi  b^3 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{280 x^5}+\frac{\pi ^2 b^5 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{840 x^3}-\frac{b \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{56 x^7}-\frac{\text{FresnelC}(b x)}{8 x^8}",1,"-(b*Cos[(b^2*Pi*x^2)/2])/(56*x^7) + (b^5*Pi^2*Cos[(b^2*Pi*x^2)/2])/(840*x^3) + (b^8*Pi^4*FresnelC[b*x])/840 - FresnelC[b*x]/(8*x^8) + (b^3*Pi*Sin[(b^2*Pi*x^2)/2])/(280*x^5) - (b^7*Pi^3*Sin[(b^2*Pi*x^2)/2])/(840*x)","A",6,4,8,0.5000,1,"{6427, 3388, 3387, 3352}"
127,1,127,0,0.1435524,"\int \frac{\text{FresnelC}(b x)}{x^{10}} \, dx","Int[FresnelC[b*x]/x^10,x]","\frac{\pi ^4 b^9 \text{CosIntegral}\left(\frac{1}{2} \pi  b^2 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  b^3 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{432 x^6}+\frac{\pi ^2 b^5 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{1728 x^4}-\frac{b \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{72 x^8}-\frac{\text{FresnelC}(b x)}{9 x^9}","\frac{\pi ^4 b^9 \text{CosIntegral}\left(\frac{1}{2} \pi  b^2 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  b^3 \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{432 x^6}+\frac{\pi ^2 b^5 \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{1728 x^4}-\frac{b \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{72 x^8}-\frac{\text{FresnelC}(b x)}{9 x^9}",1,"-(b*Cos[(b^2*Pi*x^2)/2])/(72*x^8) + (b^5*Pi^2*Cos[(b^2*Pi*x^2)/2])/(1728*x^4) + (b^9*Pi^4*CosIntegral[(b^2*Pi*x^2)/2])/6912 - FresnelC[b*x]/(9*x^9) + (b^3*Pi*Sin[(b^2*Pi*x^2)/2])/(432*x^6) - (b^7*Pi^3*Sin[(b^2*Pi*x^2)/2])/(3456*x^2)","A",7,4,8,0.5000,1,"{6427, 3380, 3297, 3302}"
128,1,298,0,0.3730601,"\int (c+d x)^3 \text{FresnelC}(a+b x) \, dx","Int[(c + d*x)^3*FresnelC[a + b*x],x]","-\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 \text{FresnelC}(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 \text{FresnelC}(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 \text{FresnelC}(a+b x)}{4 d}","-\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 \text{FresnelC}(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 \text{FresnelC}(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 \text{FresnelC}(a+b x)}{4 d}",1,"(-2*d^2*(b*c - a*d)*Cos[(Pi*(a + b*x)^2)/2])/(b^4*Pi^2) - (3*d^3*(a + b*x)*Cos[(Pi*(a + b*x)^2)/2])/(4*b^4*Pi^2) - ((b*c - a*d)^4*FresnelC[a + b*x])/(4*b^4*d) + (3*d^3*FresnelC[a + b*x])/(4*b^4*Pi^2) + ((c + d*x)^4*FresnelC[a + b*x])/(4*d) + (3*d*(b*c - a*d)^2*FresnelS[a + b*x])/(2*b^4*Pi) - ((b*c - a*d)^3*Sin[(Pi*(a + b*x)^2)/2])/(b^4*Pi) - (3*d*(b*c - a*d)^2*(a + b*x)*Sin[(Pi*(a + b*x)^2)/2])/(2*b^4*Pi) - (d^2*(b*c - a*d)*(a + b*x)^2*Sin[(Pi*(a + b*x)^2)/2])/(b^4*Pi) - (d^3*(a + b*x)^3*Sin[(Pi*(a + b*x)^2)/2])/(4*b^4*Pi)","A",14,10,14,0.7143,1,"{6429, 3434, 3352, 3380, 2637, 3386, 3351, 3296, 2638, 3385}"
129,1,194,0,0.2046144,"\int (c+d x)^2 \text{FresnelC}(a+b x) \, dx","Int[(c + d*x)^2*FresnelC[a + b*x],x]","-\frac{(b c-a d)^3 \text{FresnelC}(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 \text{FresnelC}(a+b x)}{3 d}","-\frac{(b c-a d)^3 \text{FresnelC}(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 \text{FresnelC}(a+b x)}{3 d}",1,"(-2*d^2*Cos[(Pi*(a + b*x)^2)/2])/(3*b^3*Pi^2) - ((b*c - a*d)^3*FresnelC[a + b*x])/(3*b^3*d) + ((c + d*x)^3*FresnelC[a + b*x])/(3*d) + (d*(b*c - a*d)*FresnelS[a + b*x])/(b^3*Pi) - ((b*c - a*d)^2*Sin[(Pi*(a + b*x)^2)/2])/(b^3*Pi) - (d*(b*c - a*d)*(a + b*x)*Sin[(Pi*(a + b*x)^2)/2])/(b^3*Pi) - (d^2*(a + b*x)^2*Sin[(Pi*(a + b*x)^2)/2])/(3*b^3*Pi)","A",11,9,14,0.6429,1,"{6429, 3434, 3352, 3380, 2637, 3386, 3351, 3296, 2638}"
130,1,122,0,0.1128048,"\int (c+d x) \text{FresnelC}(a+b x) \, dx","Int[(c + d*x)*FresnelC[a + b*x],x]","-\frac{(b c-a d)^2 \text{FresnelC}(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 \text{FresnelC}(a+b x)}{2 d}","-\frac{(b c-a d)^2 \text{FresnelC}(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 \text{FresnelC}(a+b x)}{2 d}",1,"-((b*c - a*d)^2*FresnelC[a + b*x])/(2*b^2*d) + ((c + d*x)^2*FresnelC[a + b*x])/(2*d) + (d*FresnelS[a + b*x])/(2*b^2*Pi) - ((b*c - a*d)*Sin[(Pi*(a + b*x)^2)/2])/(b^2*Pi) - (d*(a + b*x)*Sin[(Pi*(a + b*x)^2)/2])/(2*b^2*Pi)","A",8,7,12,0.5833,1,"{6429, 3434, 3352, 3380, 2637, 3386, 3351}"
131,1,37,0,0.0062556,"\int \text{FresnelC}(a+b x) \, dx","Int[FresnelC[a + b*x],x]","\frac{(a+b x) \text{FresnelC}(a+b x)}{b}-\frac{\sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b}","\frac{(a+b x) \text{FresnelC}(a+b x)}{b}-\frac{\sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b}",1,"((a + b*x)*FresnelC[a + b*x])/b - Sin[(Pi*(a + b*x)^2)/2]/(b*Pi)","A",1,1,6,0.1667,1,"{6419}"
132,0,0,0,0.014454,"\int \frac{\text{FresnelC}(a+b x)}{c+d x} \, dx","Int[FresnelC[a + b*x]/(c + d*x),x]","\int \frac{\text{FresnelC}(a+b x)}{c+d x} \, dx","\text{Int}\left(\frac{\text{FresnelC}(a+b x)}{c+d x},x\right)",0,"Defer[Int][FresnelC[a + b*x]/(c + d*x), x]","A",0,0,0,0,-1,"{}"
133,0,0,0,0.0142711,"\int \frac{\text{FresnelC}(a+b x)}{(c+d x)^2} \, dx","Int[FresnelC[a + b*x]/(c + d*x)^2,x]","\int \frac{\text{FresnelC}(a+b x)}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\text{FresnelC}(a+b x)}{(c+d x)^2},x\right)",0,"Defer[Int][FresnelC[a + b*x]/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
134,1,227,0,0.1871197,"\int x^3 \text{FresnelC}(a+b x) \, dx","Int[x^3*FresnelC[a + b*x],x]","-\frac{a^4 \text{FresnelC}(a+b x)}{4 b^4}+\frac{3 a^2 S(a+b x)}{2 \pi  b^4}+\frac{a^3 \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\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 \text{FresnelC}(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 \text{FresnelC}(a+b x)","-\frac{a^4 \text{FresnelC}(a+b x)}{4 b^4}+\frac{3 a^2 S(a+b x)}{2 \pi  b^4}+\frac{a^3 \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\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 \text{FresnelC}(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 \text{FresnelC}(a+b x)",1,"(2*a*Cos[(Pi*(a + b*x)^2)/2])/(b^4*Pi^2) - (3*(a + b*x)*Cos[(Pi*(a + b*x)^2)/2])/(4*b^4*Pi^2) - (a^4*FresnelC[a + b*x])/(4*b^4) + (3*FresnelC[a + b*x])/(4*b^4*Pi^2) + (x^4*FresnelC[a + b*x])/4 + (3*a^2*FresnelS[a + b*x])/(2*b^4*Pi) + (a^3*Sin[(Pi*(a + b*x)^2)/2])/(b^4*Pi) - (3*a^2*(a + b*x)*Sin[(Pi*(a + b*x)^2)/2])/(2*b^4*Pi) + (a*(a + b*x)^2*Sin[(Pi*(a + b*x)^2)/2])/(b^4*Pi) - ((a + b*x)^3*Sin[(Pi*(a + b*x)^2)/2])/(4*b^4*Pi)","A",14,10,10,1.000,1,"{6429, 3434, 3352, 3380, 2637, 3386, 3351, 3296, 2638, 3385}"
135,1,148,0,0.1225123,"\int x^2 \text{FresnelC}(a+b x) \, dx","Int[x^2*FresnelC[a + b*x],x]","\frac{a^3 \text{FresnelC}(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 \text{FresnelC}(a+b x)","\frac{a^3 \text{FresnelC}(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 \text{FresnelC}(a+b x)",1,"(-2*Cos[(Pi*(a + b*x)^2)/2])/(3*b^3*Pi^2) + (a^3*FresnelC[a + b*x])/(3*b^3) + (x^3*FresnelC[a + b*x])/3 - (a*FresnelS[a + b*x])/(b^3*Pi) - (a^2*Sin[(Pi*(a + b*x)^2)/2])/(b^3*Pi) + (a*(a + b*x)*Sin[(Pi*(a + b*x)^2)/2])/(b^3*Pi) - ((a + b*x)^2*Sin[(Pi*(a + b*x)^2)/2])/(3*b^3*Pi)","A",11,9,10,0.9000,1,"{6429, 3434, 3352, 3380, 2637, 3386, 3351, 3296, 2638}"
136,1,95,0,0.0707863,"\int x \text{FresnelC}(a+b x) \, dx","Int[x*FresnelC[a + b*x],x]","-\frac{a^2 \text{FresnelC}(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 \text{FresnelC}(a+b x)","-\frac{a^2 \text{FresnelC}(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 \text{FresnelC}(a+b x)",1,"-(a^2*FresnelC[a + b*x])/(2*b^2) + (x^2*FresnelC[a + b*x])/2 + FresnelS[a + b*x]/(2*b^2*Pi) + (a*Sin[(Pi*(a + b*x)^2)/2])/(b^2*Pi) - ((a + b*x)*Sin[(Pi*(a + b*x)^2)/2])/(2*b^2*Pi)","A",8,7,8,0.8750,1,"{6429, 3434, 3352, 3380, 2637, 3386, 3351}"
137,1,37,0,0.0067759,"\int \text{FresnelC}(a+b x) \, dx","Int[FresnelC[a + b*x],x]","\frac{(a+b x) \text{FresnelC}(a+b x)}{b}-\frac{\sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b}","\frac{(a+b x) \text{FresnelC}(a+b x)}{b}-\frac{\sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b}",1,"((a + b*x)*FresnelC[a + b*x])/b - Sin[(Pi*(a + b*x)^2)/2]/(b*Pi)","A",1,1,6,0.1667,1,"{6419}"
138,0,0,0,0.0103739,"\int \frac{\text{FresnelC}(a+b x)}{x} \, dx","Int[FresnelC[a + b*x]/x,x]","\int \frac{\text{FresnelC}(a+b x)}{x} \, dx","\text{Int}\left(\frac{\text{FresnelC}(a+b x)}{x},x\right)",0,"Defer[Int][FresnelC[a + b*x]/x, x]","A",0,0,0,0,-1,"{}"
139,0,0,0,0.0109038,"\int \frac{\text{FresnelC}(a+b x)}{x^2} \, dx","Int[FresnelC[a + b*x]/x^2,x]","\int \frac{\text{FresnelC}(a+b x)}{x^2} \, dx","\text{Int}\left(\frac{\text{FresnelC}(a+b x)}{x^2},x\right)",0,"Defer[Int][FresnelC[a + b*x]/x^2, x]","A",0,0,0,0,-1,"{}"
140,1,253,0,0.4222784,"\int x^7 \text{FresnelC}(b x)^2 \, dx","Int[x^7*FresnelC[b*x]^2,x]","-\frac{x^7 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi  b}+\frac{35 x^3 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi ^3 b^5}-\frac{7 x^5 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi ^2 b^3}+\frac{105 x \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi ^4 b^7}-\frac{105 \text{FresnelC}(b x)^2}{8 \pi ^4 b^8}+\frac{7 x^6}{48 \pi ^2 b^2}-\frac{105 x^2}{16 \pi ^4 b^6}+\frac{5 x^4 \sin \left(\pi  b^2 x^2\right)}{8 \pi ^3 b^4}-\frac{10 \sin \left(\pi  b^2 x^2\right)}{\pi ^5 b^8}-\frac{x^6 \cos \left(\pi  b^2 x^2\right)}{16 \pi ^2 b^2}+\frac{55 x^2 \cos \left(\pi  b^2 x^2\right)}{16 \pi ^4 b^6}+\frac{1}{8} x^8 \text{FresnelC}(b x)^2","-\frac{x^7 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi  b}+\frac{35 x^3 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi ^3 b^5}-\frac{7 x^5 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi ^2 b^3}+\frac{105 x \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 \pi ^4 b^7}-\frac{105 \text{FresnelC}(b x)^2}{8 \pi ^4 b^8}+\frac{7 x^6}{48 \pi ^2 b^2}-\frac{105 x^2}{16 \pi ^4 b^6}+\frac{5 x^4 \sin \left(\pi  b^2 x^2\right)}{8 \pi ^3 b^4}-\frac{10 \sin \left(\pi  b^2 x^2\right)}{\pi ^5 b^8}-\frac{x^6 \cos \left(\pi  b^2 x^2\right)}{16 \pi ^2 b^2}+\frac{55 x^2 \cos \left(\pi  b^2 x^2\right)}{16 \pi ^4 b^6}+\frac{1}{8} x^8 \text{FresnelC}(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",23,11,10,1.100,1,"{6431, 6455, 6463, 6441, 30, 3380, 2634, 3379, 3296, 2637, 3309}"
141,1,239,0,0.2982686,"\int x^6 \text{FresnelC}(b x)^2 \, dx","Int[x^6*FresnelC[b*x]^2,x]","-\frac{2 x^6 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi  b}+\frac{48 x^2 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi ^3 b^5}-\frac{12 x^4 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi ^2 b^3}+\frac{96 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi ^4 b^7}-\frac{531 \text{FresnelC}\left(\sqrt{2} b x\right)}{56 \sqrt{2} \pi ^4 b^7}+\frac{6 x^5}{35 \pi ^2 b^2}+\frac{17 x^3 \sin \left(\pi  b^2 x^2\right)}{28 \pi ^3 b^4}-\frac{x^5 \cos \left(\pi  b^2 x^2\right)}{14 \pi ^2 b^2}+\frac{21 x \cos \left(\pi  b^2 x^2\right)}{8 \pi ^4 b^6}-\frac{48 x}{7 \pi ^4 b^6}+\frac{1}{7} x^7 \text{FresnelC}(b x)^2","-\frac{2 x^6 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi  b}+\frac{48 x^2 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi ^3 b^5}-\frac{12 x^4 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi ^2 b^3}+\frac{96 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 \pi ^4 b^7}-\frac{531 \text{FresnelC}\left(\sqrt{2} b x\right)}{56 \sqrt{2} \pi ^4 b^7}+\frac{6 x^5}{35 \pi ^2 b^2}+\frac{17 x^3 \sin \left(\pi  b^2 x^2\right)}{28 \pi ^3 b^4}-\frac{x^5 \cos \left(\pi  b^2 x^2\right)}{14 \pi ^2 b^2}+\frac{21 x \cos \left(\pi  b^2 x^2\right)}{8 \pi ^4 b^6}-\frac{48 x}{7 \pi ^4 b^6}+\frac{1}{7} x^7 \text{FresnelC}(b x)^2",1,"(-48*x)/(7*b^6*Pi^4) + (6*x^5)/(35*b^2*Pi^2) + (21*x*Cos[b^2*Pi*x^2])/(8*b^6*Pi^4) - (x^5*Cos[b^2*Pi*x^2])/(14*b^2*Pi^2) + (96*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(7*b^7*Pi^4) - (12*x^4*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(7*b^3*Pi^2) + (x^7*FresnelC[b*x]^2)/7 - (531*FresnelC[Sqrt[2]*b*x])/(56*Sqrt[2]*b^7*Pi^4) + (48*x^2*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(7*b^5*Pi^3) - (2*x^6*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(7*b*Pi) + (17*x^3*Sin[b^2*Pi*x^2])/(28*b^4*Pi^3)","A",19,10,10,1.000,1,"{6431, 6455, 6463, 6461, 3358, 3352, 3385, 3392, 30, 3386}"
142,1,265,0,0.2883273,"\int x^5 \text{FresnelC}(b x)^2 \, dx","Int[x^5*FresnelC[b*x]^2,x]","-\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 \text{FresnelC}(b x) S(b x)}{2 \pi ^3 b^6}-\frac{x^5 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 \pi  b}+\frac{5 x \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^5}-\frac{5 x^3 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 \pi ^2 b^3}+\frac{5 x^4}{24 \pi ^2 b^2}+\frac{7 x^2 \sin \left(\pi  b^2 x^2\right)}{12 \pi ^3 b^4}-\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{1}{6} x^6 \text{FresnelC}(b x)^2","-\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 \text{FresnelC}(b x) S(b x)}{2 \pi ^3 b^6}-\frac{x^5 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 \pi  b}+\frac{5 x \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^5}-\frac{5 x^3 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 \pi ^2 b^3}+\frac{5 x^4}{24 \pi ^2 b^2}+\frac{7 x^2 \sin \left(\pi  b^2 x^2\right)}{12 \pi ^3 b^4}-\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{1}{6} x^6 \text{FresnelC}(b x)^2",1,"(5*x^4)/(24*b^2*Pi^2) + (11*Cos[b^2*Pi*x^2])/(6*b^6*Pi^4) - (x^4*Cos[b^2*Pi*x^2])/(12*b^2*Pi^2) - (5*x^3*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(3*b^3*Pi^2) + (x^6*FresnelC[b*x]^2)/6 - (5*FresnelC[b*x]*FresnelS[b*x])/(2*b^6*Pi^3) - (((5*I)/8)*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (-I/2)*b^2*Pi*x^2])/(b^4*Pi^3) + (((5*I)/8)*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (I/2)*b^2*Pi*x^2])/(b^4*Pi^3) + (5*x*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^5*Pi^3) - (x^5*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(3*b*Pi) + (7*x^2*Sin[b^2*Pi*x^2])/(12*b^4*Pi^3)","A",16,10,10,1.000,1,"{6431, 6455, 6463, 6447, 3379, 2638, 3380, 3309, 30, 3296}"
143,1,177,0,0.1879877,"\int x^4 \text{FresnelC}(b x)^2 \, dx","Int[x^4*FresnelC[b*x]^2,x]","-\frac{2 x^4 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 \pi  b}+\frac{16 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 \pi ^3 b^5}-\frac{8 x^2 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 \pi ^2 b^3}-\frac{43 S\left(\sqrt{2} b x\right)}{20 \sqrt{2} \pi ^3 b^5}+\frac{4 x^3}{15 \pi ^2 b^2}+\frac{11 x \sin \left(\pi  b^2 x^2\right)}{20 \pi ^3 b^4}-\frac{x^3 \cos \left(\pi  b^2 x^2\right)}{10 \pi ^2 b^2}+\frac{1}{5} x^5 \text{FresnelC}(b x)^2","-\frac{2 x^4 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 \pi  b}+\frac{16 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 \pi ^3 b^5}-\frac{8 x^2 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 \pi ^2 b^3}-\frac{43 S\left(\sqrt{2} b x\right)}{20 \sqrt{2} \pi ^3 b^5}+\frac{4 x^3}{15 \pi ^2 b^2}+\frac{11 x \sin \left(\pi  b^2 x^2\right)}{20 \pi ^3 b^4}-\frac{x^3 \cos \left(\pi  b^2 x^2\right)}{10 \pi ^2 b^2}+\frac{1}{5} x^5 \text{FresnelC}(b x)^2",1,"(4*x^3)/(15*b^2*Pi^2) - (x^3*Cos[b^2*Pi*x^2])/(10*b^2*Pi^2) - (8*x^2*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(5*b^3*Pi^2) + (x^5*FresnelC[b*x]^2)/5 - (43*FresnelS[Sqrt[2]*b*x])/(20*Sqrt[2]*b^5*Pi^3) + (16*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(5*b^5*Pi^3) - (2*x^4*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(5*b*Pi) + (11*x*Sin[b^2*Pi*x^2])/(20*b^4*Pi^3)","A",12,9,10,0.9000,1,"{6431, 6455, 6463, 6453, 3351, 3392, 30, 3386, 3385}"
144,1,140,0,0.1558162,"\int x^3 \text{FresnelC}(b x)^2 \, dx","Int[x^3*FresnelC[b*x]^2,x]","-\frac{x^3 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{2 \pi  b}-\frac{3 x \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{2 \pi ^2 b^3}+\frac{3 \text{FresnelC}(b x)^2}{4 \pi ^2 b^4}+\frac{3 x^2}{8 \pi ^2 b^2}+\frac{\sin \left(\pi  b^2 x^2\right)}{2 \pi ^3 b^4}-\frac{x^2 \cos \left(\pi  b^2 x^2\right)}{8 \pi ^2 b^2}+\frac{1}{4} x^4 \text{FresnelC}(b x)^2","-\frac{x^3 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{2 \pi  b}-\frac{3 x \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{2 \pi ^2 b^3}+\frac{3 \text{FresnelC}(b x)^2}{4 \pi ^2 b^4}+\frac{3 x^2}{8 \pi ^2 b^2}+\frac{\sin \left(\pi  b^2 x^2\right)}{2 \pi ^3 b^4}-\frac{x^2 \cos \left(\pi  b^2 x^2\right)}{8 \pi ^2 b^2}+\frac{1}{4} x^4 \text{FresnelC}(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",10,10,10,1.000,1,"{6431, 6455, 6463, 6441, 30, 3380, 2634, 3379, 3296, 2637}"
145,1,124,0,0.1053121,"\int x^2 \text{FresnelC}(b x)^2 \, dx","Int[x^2*FresnelC[b*x]^2,x]","-\frac{2 x^2 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 \pi  b}-\frac{4 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 \pi ^2 b^3}+\frac{5 \text{FresnelC}\left(\sqrt{2} b x\right)}{6 \sqrt{2} \pi ^2 b^3}-\frac{x \cos \left(\pi  b^2 x^2\right)}{6 \pi ^2 b^2}+\frac{2 x}{3 \pi ^2 b^2}+\frac{1}{3} x^3 \text{FresnelC}(b x)^2","-\frac{2 x^2 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 \pi  b}-\frac{4 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 \pi ^2 b^3}+\frac{5 \text{FresnelC}\left(\sqrt{2} b x\right)}{6 \sqrt{2} \pi ^2 b^3}-\frac{x \cos \left(\pi  b^2 x^2\right)}{6 \pi ^2 b^2}+\frac{2 x}{3 \pi ^2 b^2}+\frac{1}{3} x^3 \text{FresnelC}(b x)^2",1,"(2*x)/(3*b^2*Pi^2) - (x*Cos[b^2*Pi*x^2])/(6*b^2*Pi^2) - (4*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(3*b^3*Pi^2) + (x^3*FresnelC[b*x]^2)/3 + (5*FresnelC[Sqrt[2]*b*x])/(6*Sqrt[2]*b^3*Pi^2) - (2*x^2*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(3*b*Pi)","A",8,6,10,0.6000,1,"{6431, 6455, 6461, 3358, 3352, 3385}"
146,1,144,0,0.0839067,"\int x \text{FresnelC}(b x)^2 \, dx","Int[x*FresnelC[b*x]^2,x]","\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{\text{FresnelC}(b x) S(b x)}{2 \pi  b^2}-\frac{x \text{FresnelC}(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 \text{FresnelC}(b x)^2","\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{\text{FresnelC}(b x) S(b x)}{2 \pi  b^2}-\frac{x \text{FresnelC}(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 \text{FresnelC}(b x)^2",1,"-Cos[b^2*Pi*x^2]/(4*b^2*Pi^2) + (x^2*FresnelC[b*x]^2)/2 + (FresnelC[b*x]*FresnelS[b*x])/(2*b^2*Pi) + ((I/8)*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (-I/2)*b^2*Pi*x^2])/Pi - ((I/8)*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (I/2)*b^2*Pi*x^2])/Pi - (x*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(b*Pi)","A",5,5,8,0.6250,1,"{6431, 6455, 6447, 3379, 2638}"
147,1,54,0,0.0360543,"\int \text{FresnelC}(b x)^2 \, dx","Int[FresnelC[b*x]^2,x]","-\frac{2 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b}+x \text{FresnelC}(b x)^2+\frac{S\left(\sqrt{2} b x\right)}{\sqrt{2} \pi  b}","-\frac{2 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b}+x \text{FresnelC}(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",4,4,6,0.6667,1,"{6421, 12, 6453, 3351}"
148,0,0,0,0.0161198,"\int \frac{\text{FresnelC}(b x)^2}{x} \, dx","Int[FresnelC[b*x]^2/x,x]","\int \frac{\text{FresnelC}(b x)^2}{x} \, dx","\text{Int}\left(\frac{\text{FresnelC}(b x)^2}{x},x\right)",0,"Defer[Int][FresnelC[b*x]^2/x, x]","A",0,0,0,0,-1,"{}"
149,0,0,0,0.0373831,"\int \frac{\text{FresnelC}(b x)^2}{x^2} \, dx","Int[FresnelC[b*x]^2/x^2,x]","\int \frac{\text{FresnelC}(b x)^2}{x^2} \, dx","2 b \text{Int}\left(\frac{\text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)-\frac{\text{FresnelC}(b x)^2}{x}",0,"-(FresnelC[b*x]^2/x) + 2*b*Defer[Int][(Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/x, x]","A",0,0,0,0,-1,"{}"
150,0,0,0,0.0371539,"\int \frac{\text{FresnelC}(b x)^2}{x^3} \, dx","Int[FresnelC[b*x]^2/x^3,x]","\int \frac{\text{FresnelC}(b x)^2}{x^3} \, dx","b \text{Int}\left(\frac{\text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x^2},x\right)-\frac{\text{FresnelC}(b x)^2}{2 x^2}",0,"-FresnelC[b*x]^2/(2*x^2) + b*Defer[Int][(Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/x^2, x]","A",0,0,0,0,-1,"{}"
151,0,0,0,0.0828138,"\int \frac{\text{FresnelC}(b x)^2}{x^4} \, dx","Int[FresnelC[b*x]^2/x^4,x]","\int \frac{\text{FresnelC}(b x)^2}{x^4} \, dx","-\frac{1}{3} \pi  b^3 \text{Int}\left(\frac{\text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)-\frac{b \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 x^2}-\frac{\pi  b^3 S\left(\sqrt{2} b x\right)}{3 \sqrt{2}}-\frac{b^2 \cos \left(\pi  b^2 x^2\right)}{6 x}-\frac{b^2}{6 x}-\frac{\text{FresnelC}(b x)^2}{3 x^3}",0,"-b^2/(6*x) - (b^2*Cos[b^2*Pi*x^2])/(6*x) - (b*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(3*x^2) - FresnelC[b*x]^2/(3*x^3) - (b^3*Pi*FresnelS[Sqrt[2]*b*x])/(3*Sqrt[2]) - (b^3*Pi*Defer[Int][(FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/x, x])/3","A",0,0,0,0,-1,"{}"
152,1,127,0,0.1378776,"\int \frac{\text{FresnelC}(b x)^2}{x^5} \, dx","Int[FresnelC[b*x]^2/x^5,x]","\frac{\pi  b^3 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 x}-\frac{b \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 x^3}-\frac{1}{12} \pi ^2 b^4 \text{FresnelC}(b x)^2-\frac{1}{12} \pi  b^4 \text{Si}\left(b^2 \pi  x^2\right)-\frac{b^2}{24 x^2}-\frac{b^2 \cos \left(\pi  b^2 x^2\right)}{24 x^2}-\frac{\text{FresnelC}(b x)^2}{4 x^4}","\frac{\pi  b^3 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 x}-\frac{b \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 x^3}-\frac{1}{12} \pi ^2 b^4 \text{FresnelC}(b x)^2-\frac{1}{12} \pi  b^4 \text{Si}\left(b^2 \pi  x^2\right)-\frac{b^2}{24 x^2}-\frac{b^2 \cos \left(\pi  b^2 x^2\right)}{24 x^2}-\frac{\text{FresnelC}(b x)^2}{4 x^4}",1,"-b^2/(24*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",9,9,10,0.9000,1,"{6431, 6457, 6465, 6441, 30, 3375, 3380, 3297, 3299}"
153,0,0,0,0.1452678,"\int \frac{\text{FresnelC}(b x)^2}{x^6} \, dx","Int[FresnelC[b*x]^2/x^6,x]","\int \frac{\text{FresnelC}(b x)^2}{x^6} \, dx","-\frac{1}{20} \pi ^2 b^5 \text{Int}\left(\frac{\text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)+\frac{\pi  b^3 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{20 x^2}-\frac{b \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{10 x^4}-\frac{7 \pi ^2 b^5 \text{FresnelC}\left(\sqrt{2} b x\right)}{60 \sqrt{2}}-\frac{b^2}{60 x^3}+\frac{7 \pi  b^4 \sin \left(\pi  b^2 x^2\right)}{120 x}-\frac{b^2 \cos \left(\pi  b^2 x^2\right)}{60 x^3}-\frac{\text{FresnelC}(b x)^2}{5 x^5}",0,"-b^2/(60*x^3) - (b^2*Cos[b^2*Pi*x^2])/(60*x^3) - (b*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(10*x^4) - FresnelC[b*x]^2/(5*x^5) - (7*b^5*Pi^2*FresnelC[Sqrt[2]*b*x])/(60*Sqrt[2]) + (b^3*Pi*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(20*x^2) + (7*b^4*Pi*Sin[b^2*Pi*x^2])/(120*x) - (b^5*Pi^2*Defer[Int][(Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/x, x])/20","A",0,0,0,0,-1,"{}"
154,0,0,0,0.2202583,"\int \frac{\text{FresnelC}(b x)^2}{x^7} \, dx","Int[FresnelC[b*x]^2/x^7,x]","\int \frac{\text{FresnelC}(b x)^2}{x^7} \, dx","-\frac{1}{45} \pi ^2 b^5 \text{Int}\left(\frac{\text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x^2},x\right)-\frac{1}{72} \pi ^2 b^6 \text{CosIntegral}\left(\pi  b^2 x^2\right)+\frac{\pi  b^3 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{45 x^3}-\frac{b \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{15 x^5}-\frac{b^2}{120 x^4}+\frac{\pi  b^4 \sin \left(\pi  b^2 x^2\right)}{72 x^2}-\frac{b^2 \cos \left(\pi  b^2 x^2\right)}{120 x^4}-\frac{\text{FresnelC}(b x)^2}{6 x^6}",0,"-b^2/(120*x^4) - (b^2*Cos[b^2*Pi*x^2])/(120*x^4) - (b^6*Pi^2*CosIntegral[b^2*Pi*x^2])/72 - (b*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(15*x^5) - FresnelC[b*x]^2/(6*x^6) + (b^3*Pi*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(45*x^3) + (b^4*Pi*Sin[b^2*Pi*x^2])/(72*x^2) - (b^5*Pi^2*Defer[Int][(Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/x^2, x])/45","A",0,0,0,0,-1,"{}"
155,0,0,0,0.2397434,"\int \frac{\text{FresnelC}(b x)^2}{x^8} \, dx","Int[FresnelC[b*x]^2/x^8,x]","\int \frac{\text{FresnelC}(b x)^2}{x^8} \, dx","\frac{1}{168} \pi ^3 b^7 \text{Int}\left(\frac{\text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)+\frac{\pi  b^3 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{84 x^4}+\frac{\pi ^2 b^5 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{168 x^2}-\frac{b \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{21 x^6}+\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{b^2}{210 x^5}+\frac{13 \pi  b^4 \sin \left(\pi  b^2 x^2\right)}{2520 x^3}+\frac{67 \pi ^2 b^6 \cos \left(\pi  b^2 x^2\right)}{5040 x}-\frac{b^2 \cos \left(\pi  b^2 x^2\right)}{210 x^5}+\frac{\pi ^2 b^6}{336 x}-\frac{\text{FresnelC}(b x)^2}{7 x^7}",0,"-b^2/(210*x^5) + (b^6*Pi^2)/(336*x) - (b^2*Cos[b^2*Pi*x^2])/(210*x^5) + (67*b^6*Pi^2*Cos[b^2*Pi*x^2])/(5040*x) - (b*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(21*x^6) + (b^5*Pi^2*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(168*x^2) - FresnelC[b*x]^2/(7*x^7) + (b^7*Pi^3*FresnelS[Sqrt[2]*b*x])/(72*Sqrt[2]) + (2*Sqrt[2]*b^7*Pi^3*FresnelS[Sqrt[2]*b*x])/315 + (b^3*Pi*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(84*x^4) + (13*b^4*Pi*Sin[b^2*Pi*x^2])/(2520*x^3) + (b^7*Pi^3*Defer[Int][(FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/x, x])/168","A",0,0,0,0,-1,"{}"
156,1,242,0,0.3880836,"\int \frac{\text{FresnelC}(b x)^2}{x^9} \, dx","Int[FresnelC[b*x]^2/x^9,x]","-\frac{\pi ^3 b^7 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{420 x}+\frac{\pi  b^3 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{140 x^5}+\frac{\pi ^2 b^5 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{420 x^3}-\frac{b \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{28 x^7}+\frac{1}{840} \pi ^4 b^8 \text{FresnelC}(b x)^2+\frac{1}{280} \pi ^3 b^8 \text{Si}\left(b^2 \pi  x^2\right)+\frac{\pi ^2 b^6}{1680 x^2}-\frac{b^2}{336 x^6}+\frac{\pi  b^4 \sin \left(\pi  b^2 x^2\right)}{420 x^4}+\frac{\pi ^2 b^6 \cos \left(\pi  b^2 x^2\right)}{336 x^2}-\frac{b^2 \cos \left(\pi  b^2 x^2\right)}{336 x^6}-\frac{\text{FresnelC}(b x)^2}{8 x^8}","-\frac{\pi ^3 b^7 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{420 x}+\frac{\pi  b^3 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{140 x^5}+\frac{\pi ^2 b^5 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{420 x^3}-\frac{b \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{28 x^7}+\frac{1}{840} \pi ^4 b^8 \text{FresnelC}(b x)^2+\frac{1}{280} \pi ^3 b^8 \text{Si}\left(b^2 \pi  x^2\right)+\frac{\pi ^2 b^6}{1680 x^2}-\frac{b^2}{336 x^6}+\frac{\pi  b^4 \sin \left(\pi  b^2 x^2\right)}{420 x^4}+\frac{\pi ^2 b^6 \cos \left(\pi  b^2 x^2\right)}{336 x^2}-\frac{b^2 \cos \left(\pi  b^2 x^2\right)}{336 x^6}-\frac{\text{FresnelC}(b x)^2}{8 x^8}",1,"-b^2/(336*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",20,10,10,1.000,1,"{6431, 6457, 6465, 6441, 30, 3375, 3380, 3297, 3299, 3379}"
157,0,0,0,0.3421146,"\int \frac{\text{FresnelC}(b x)^2}{x^{10}} \, dx","Int[FresnelC[b*x]^2/x^10,x]","\int \frac{\text{FresnelC}(b x)^2}{x^{10}} \, dx","\frac{\pi ^4 b^9 \text{Int}\left(\frac{\text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)}{1728}-\frac{\pi ^3 b^7 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{1728 x^2}+\frac{\pi  b^3 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{216 x^6}+\frac{\pi ^2 b^5 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{864 x^4}-\frac{b \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{36 x^8}+\frac{853 \pi ^4 b^9 \text{FresnelC}\left(\sqrt{2} b x\right)}{181440 \sqrt{2}}+\frac{\pi ^2 b^6}{5184 x^3}-\frac{b^2}{504 x^7}-\frac{853 \pi ^3 b^8 \sin \left(\pi  b^2 x^2\right)}{362880 x}+\frac{19 \pi  b^4 \sin \left(\pi  b^2 x^2\right)}{15120 x^5}+\frac{187 \pi ^2 b^6 \cos \left(\pi  b^2 x^2\right)}{181440 x^3}-\frac{b^2 \cos \left(\pi  b^2 x^2\right)}{504 x^7}-\frac{\text{FresnelC}(b x)^2}{9 x^9}",0,"-b^2/(504*x^7) + (b^6*Pi^2)/(5184*x^3) - (b^2*Cos[b^2*Pi*x^2])/(504*x^7) + (187*b^6*Pi^2*Cos[b^2*Pi*x^2])/(181440*x^3) - (b*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(36*x^8) + (b^5*Pi^2*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(864*x^4) - FresnelC[b*x]^2/(9*x^9) + (853*b^9*Pi^4*FresnelC[Sqrt[2]*b*x])/(181440*Sqrt[2]) + (b^3*Pi*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(216*x^6) - (b^7*Pi^3*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(1728*x^2) + (19*b^4*Pi*Sin[b^2*Pi*x^2])/(15120*x^5) - (853*b^8*Pi^3*Sin[b^2*Pi*x^2])/(362880*x) + (b^9*Pi^4*Defer[Int][(Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/x, x])/1728","A",0,0,0,0,-1,"{}"
158,1,495,0,0.3962931,"\int (c+d x)^2 \text{FresnelC}(a+b x)^2 \, dx","Int[(c + d*x)^2*FresnelC[a + b*x]^2,x]","\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) \text{FresnelC}(a+b x) S(a+b x)}{\pi  b^3}+\frac{d (a+b x)^2 (b c-a d) \text{FresnelC}(a+b x)^2}{b^3}+\frac{(a+b x) (b c-a d)^2 \text{FresnelC}(a+b x)^2}{b^3}-\frac{2 d (a+b x) (b c-a d) \text{FresnelC}(a+b x) \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b^3}-\frac{2 (b c-a d)^2 \text{FresnelC}(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 \text{FresnelC}(a+b x)^2}{3 b^3}+\frac{5 d^2 \text{FresnelC}\left(\sqrt{2} (a+b x)\right)}{6 \sqrt{2} \pi ^2 b^3}-\frac{2 d^2 (a+b x)^2 \text{FresnelC}(a+b x) \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{3 \pi  b^3}-\frac{4 d^2 \text{FresnelC}(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}","\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) \text{FresnelC}(a+b x) S(a+b x)}{\pi  b^3}+\frac{d (a+b x)^2 (b c-a d) \text{FresnelC}(a+b x)^2}{b^3}+\frac{(a+b x) (b c-a d)^2 \text{FresnelC}(a+b x)^2}{b^3}-\frac{2 d (a+b x) (b c-a d) \text{FresnelC}(a+b x) \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{\pi  b^3}-\frac{2 (b c-a d)^2 \text{FresnelC}(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 \text{FresnelC}(a+b x)^2}{3 b^3}+\frac{5 d^2 \text{FresnelC}\left(\sqrt{2} (a+b x)\right)}{6 \sqrt{2} \pi ^2 b^3}-\frac{2 d^2 (a+b x)^2 \text{FresnelC}(a+b x) \sin \left(\frac{1}{2} \pi  (a+b x)^2\right)}{3 \pi  b^3}-\frac{4 d^2 \text{FresnelC}(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,"(2*d^2*x)/(3*b^2*Pi^2) - (d*(b*c - a*d)*Cos[Pi*(a + b*x)^2])/(2*b^3*Pi^2) - (d^2*(a + b*x)*Cos[Pi*(a + b*x)^2])/(6*b^3*Pi^2) - (4*d^2*Cos[(Pi*(a + b*x)^2)/2]*FresnelC[a + b*x])/(3*b^3*Pi^2) + ((b*c - a*d)^2*(a + b*x)*FresnelC[a + b*x]^2)/b^3 + (d*(b*c - a*d)*(a + b*x)^2*FresnelC[a + b*x]^2)/b^3 + (d^2*(a + b*x)^3*FresnelC[a + b*x]^2)/(3*b^3) + (5*d^2*FresnelC[Sqrt[2]*(a + b*x)])/(6*Sqrt[2]*b^3*Pi^2) + (d*(b*c - a*d)*FresnelC[a + b*x]*FresnelS[a + b*x])/(b^3*Pi) + ((b*c - a*d)^2*FresnelS[Sqrt[2]*(a + b*x)])/(Sqrt[2]*b^3*Pi) + ((I/4)*d*(b*c - a*d)*(a + b*x)^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (-I/2)*Pi*(a + b*x)^2])/(b^3*Pi) - ((I/4)*d*(b*c - a*d)*(a + b*x)^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (I/2)*Pi*(a + b*x)^2])/(b^3*Pi) - (2*(b*c - a*d)^2*FresnelC[a + b*x]*Sin[(Pi*(a + b*x)^2)/2])/(b^3*Pi) - (2*d*(b*c - a*d)*(a + b*x)*FresnelC[a + b*x]*Sin[(Pi*(a + b*x)^2)/2])/(b^3*Pi) - (2*d^2*(a + b*x)^2*FresnelC[a + b*x]*Sin[(Pi*(a + b*x)^2)/2])/(3*b^3*Pi)","A",18,13,16,0.8125,1,"{6433, 6421, 6453, 3351, 6431, 6455, 6447, 3379, 2638, 6461, 3358, 3352, 3385}"
159,1,279,0,0.1851266,"\int (c+d x) \text{FresnelC}(a+b x)^2 \, dx","Int[(c + d*x)*FresnelC[a + b*x]^2,x]","\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) \text{FresnelC}(a+b x)^2}{b^2}-\frac{2 (b c-a d) \text{FresnelC}(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 \text{FresnelC}(a+b x) S(a+b x)}{2 \pi  b^2}+\frac{d (a+b x)^2 \text{FresnelC}(a+b x)^2}{2 b^2}-\frac{d (a+b x) \text{FresnelC}(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}","\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) \text{FresnelC}(a+b x)^2}{b^2}-\frac{2 (b c-a d) \text{FresnelC}(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 \text{FresnelC}(a+b x) S(a+b x)}{2 \pi  b^2}+\frac{d (a+b x)^2 \text{FresnelC}(a+b x)^2}{2 b^2}-\frac{d (a+b x) \text{FresnelC}(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,"-(d*Cos[Pi*(a + b*x)^2])/(4*b^2*Pi^2) + ((b*c - a*d)*(a + b*x)*FresnelC[a + b*x]^2)/b^2 + (d*(a + b*x)^2*FresnelC[a + b*x]^2)/(2*b^2) + (d*FresnelC[a + b*x]*FresnelS[a + b*x])/(2*b^2*Pi) + ((b*c - a*d)*FresnelS[Sqrt[2]*(a + b*x)])/(Sqrt[2]*b^2*Pi) + ((I/8)*d*(a + b*x)^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (-I/2)*Pi*(a + b*x)^2])/(b^2*Pi) - ((I/8)*d*(a + b*x)^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (I/2)*Pi*(a + b*x)^2])/(b^2*Pi) - (2*(b*c - a*d)*FresnelC[a + b*x]*Sin[(Pi*(a + b*x)^2)/2])/(b^2*Pi) - (d*(a + b*x)*FresnelC[a + b*x]*Sin[(Pi*(a + b*x)^2)/2])/(b^2*Pi)","A",10,9,14,0.6429,1,"{6433, 6421, 6453, 3351, 6431, 6455, 6447, 3379, 2638}"
160,1,69,0,0.1506859,"\int \text{FresnelC}(a+b x)^2 \, dx","Int[FresnelC[a + b*x]^2,x]","\frac{(a+b x) \text{FresnelC}(a+b x)^2}{b}-\frac{2 \text{FresnelC}(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}","\frac{(a+b x) \text{FresnelC}(a+b x)^2}{b}-\frac{2 \text{FresnelC}(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,"((a + b*x)*FresnelC[a + b*x]^2)/b + FresnelS[Sqrt[2]*(a + b*x)]/(Sqrt[2]*b*Pi) - (2*FresnelC[a + b*x]*Sin[(Pi*(a + b*x)^2)/2])/(b*Pi)","A",4,3,8,0.3750,1,"{6421, 6453, 3351}"
161,0,0,0,0.023169,"\int \frac{\text{FresnelC}(a+b x)^2}{c+d x} \, dx","Int[FresnelC[a + b*x]^2/(c + d*x),x]","\int \frac{\text{FresnelC}(a+b x)^2}{c+d x} \, dx","\text{Int}\left(\frac{\text{FresnelC}(a+b x)^2}{c+d x},x\right)",0,"Defer[Int][FresnelC[a + b*x]^2/(c + d*x), x]","A",0,0,0,0,-1,"{}"
162,0,0,0,0.0228539,"\int \frac{\text{FresnelC}(a+b x)^2}{(c+d x)^2} \, dx","Int[FresnelC[a + b*x]^2/(c + d*x)^2,x]","\int \frac{\text{FresnelC}(a+b x)^2}{(c+d x)^2} \, dx","\text{Int}\left(\frac{\text{FresnelC}(a+b x)^2}{(c+d x)^2},x\right)",0,"Defer[Int][FresnelC[a + b*x]^2/(c + d*x)^2, x]","A",0,0,0,0,-1,"{}"
163,1,231,0,0.5222685,"\int x^2 \text{FresnelC}\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[x^2*FresnelC[d*(a + b*Log[c*x^n])],x]","\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 \text{FresnelC}\left(d \left(a+b \log \left(c x^n\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 \text{FresnelC}\left(d \left(a+b \log \left(c x^n\right)\right)\right)",1,"((1/12 + I/12)*E^((-3*a)/(b*n) + ((9*I)/2)/(b^2*d^2*n^2*Pi))*x^3*Erf[((1/2 + I/2)*(3/n + I*a*b*d^2*Pi + I*b^2*d^2*Pi*Log[c*x^n]))/(b*d*Sqrt[Pi])])/(c*x^n)^(3/n) - ((1/12 + I/12)*E^((-3*a)/(b*n) - ((9*I)/2)/(b^2*d^2*n^2*Pi))*x^3*Erfi[((1/2 + I/2)*(3/n - I*a*b*d^2*Pi - I*b^2*d^2*Pi*Log[c*x^n]))/(b*d*Sqrt[Pi])])/(c*x^n)^(3/n) + (x^3*FresnelC[d*(a + b*Log[c*x^n])])/3","A",14,9,17,0.5294,1,"{6472, 4618, 2278, 2274, 15, 2276, 2234, 2204, 2205}"
164,1,227,0,0.4078774,"\int x \text{FresnelC}\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[x*FresnelC[d*(a + b*Log[c*x^n])],x]","\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 \text{FresnelC}\left(d \left(a+b \log \left(c x^n\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 \text{FresnelC}\left(d \left(a+b \log \left(c x^n\right)\right)\right)",1,"((1/8 + I/8)*E^((2*I - 2*a*b*d^2*n*Pi)/(b^2*d^2*n^2*Pi))*x^2*Erf[((1/2 + I/2)*(2/n + I*a*b*d^2*Pi + I*b^2*d^2*Pi*Log[c*x^n]))/(b*d*Sqrt[Pi])])/(c*x^n)^(2/n) - ((1/8 + I/8)*x^2*Erfi[((1/2 + I/2)*(2/n - I*a*b*d^2*Pi - I*b^2*d^2*Pi*Log[c*x^n]))/(b*d*Sqrt[Pi])])/(E^((2*(I + a*b*d^2*n*Pi))/(b^2*d^2*n^2*Pi))*(c*x^n)^(2/n)) + (x^2*FresnelC[d*(a + b*Log[c*x^n])])/2","A",14,9,15,0.6000,1,"{6472, 4618, 2278, 2274, 15, 2276, 2234, 2204, 2205}"
165,1,214,0,0.2634217,"\int \text{FresnelC}\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[FresnelC[d*(a + b*Log[c*x^n])],x]","\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 \text{FresnelC}\left(d \left(a+b \log \left(c x^n\right)\right)\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{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 \text{FresnelC}\left(d \left(a+b \log \left(c x^n\right)\right)\right)",1,"((1/4 + I/4)*x*Erf[((1/2 + I/2)*(n^(-1) + I*a*b*d^2*Pi + I*b^2*d^2*Pi*Log[c*x^n]))/(b*d*Sqrt[Pi])])/(E^((2*a*b*n - I/(d^2*Pi))/(2*b^2*n^2))*(c*x^n)^n^(-1)) - ((1/4 + I/4)*x*Erfi[((1/2 + I/2)*(n^(-1) - I*a*b*d^2*Pi - I*b^2*d^2*Pi*Log[c*x^n]))/(b*d*Sqrt[Pi])])/(E^((2*a*b*n + I/(d^2*Pi))/(2*b^2*n^2))*(c*x^n)^n^(-1)) + x*FresnelC[d*(a + b*Log[c*x^n])]","A",14,9,13,0.6923,1,"{6469, 4616, 2277, 2274, 15, 2276, 2234, 2204, 2205}"
166,1,66,0,0.0399113,"\int \frac{\text{FresnelC}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x} \, dx","Int[FresnelC[d*(a + b*Log[c*x^n])]/x,x]","\frac{\left(a+b \log \left(c x^n\right)\right) \text{FresnelC}\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}","\frac{\left(a+b \log \left(c x^n\right)\right) \text{FresnelC}\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,"(FresnelC[d*(a + b*Log[c*x^n])]*(a + b*Log[c*x^n]))/(b*n) - Sin[(d^2*Pi*(a + b*Log[c*x^n])^2)/2]/(b*d*n*Pi)","A",3,1,17,0.05882,1,"{6419}"
167,1,217,0,0.4925603,"\int \frac{\text{FresnelC}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^2} \, dx","Int[FresnelC[d*(a + b*Log[c*x^n])]/x^2,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{\text{FresnelC}\left(d \left(a+b \log \left(c x^n\right)\right)\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{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{\text{FresnelC}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x}",1,"((1/4 + I/4)*E^((2*a*b*n + I/(d^2*Pi))/(2*b^2*n^2))*(c*x^n)^n^(-1)*Erf[((1/2 + I/2)*(n^(-1) - I*a*b*d^2*Pi - I*b^2*d^2*Pi*Log[c*x^n]))/(b*d*Sqrt[Pi])])/x - ((1/4 + I/4)*E^((2*a*b*n - I/(d^2*Pi))/(2*b^2*n^2))*(c*x^n)^n^(-1)*Erfi[((1/2 + I/2)*(n^(-1) + I*a*b*d^2*Pi + I*b^2*d^2*Pi*Log[c*x^n]))/(b*d*Sqrt[Pi])])/x - FresnelC[d*(a + b*Log[c*x^n])]/x","A",14,9,17,0.5294,1,"{6472, 4618, 2278, 2274, 15, 2276, 2234, 2204, 2205}"
168,1,228,0,0.4931256,"\int \frac{\text{FresnelC}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{x^3} \, dx","Int[FresnelC[d*(a + b*Log[c*x^n])]/x^3,x]","\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{\text{FresnelC}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{2 x^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{\text{FresnelC}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{2 x^2}",1,"((1/8 + I/8)*E^((2*I + 2*a*b*d^2*n*Pi)/(b^2*d^2*n^2*Pi))*(c*x^n)^(2/n)*Erf[((1/2 + I/2)*(2/n - I*a*b*d^2*Pi - I*b^2*d^2*Pi*Log[c*x^n]))/(b*d*Sqrt[Pi])])/x^2 - ((1/8 + I/8)*(c*x^n)^(2/n)*Erfi[((1/2 + I/2)*(2/n + I*a*b*d^2*Pi + I*b^2*d^2*Pi*Log[c*x^n]))/(b*d*Sqrt[Pi])])/(E^((2*(I - a*b*d^2*n*Pi))/(b^2*d^2*n^2*Pi))*x^2) - FresnelC[d*(a + b*Log[c*x^n])]/(2*x^2)","A",14,9,17,0.5294,1,"{6472, 4618, 2278, 2274, 15, 2276, 2234, 2204, 2205}"
169,1,280,0,0.6070059,"\int (e x)^m \text{FresnelC}\left(d \left(a+b \log \left(c x^n\right)\right)\right) \, dx","Int[(e*x)^m*FresnelC[d*(a + b*Log[c*x^n])],x]","\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} \text{FresnelC}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e (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} \text{FresnelC}\left(d \left(a+b \log \left(c x^n\right)\right)\right)}{e (m+1)}",1,"((1/4 + I/4)*E^(((I/2)*(1 + m)*(1 + m + (2*I)*a*b*d^2*n*Pi))/(b^2*d^2*n^2*Pi))*x*(e*x)^m*Erf[((1/2 + I/2)*(1 + m + I*a*b*d^2*n*Pi + I*b^2*d^2*n*Pi*Log[c*x^n]))/(b*d*n*Sqrt[Pi])])/((1 + m)*(c*x^n)^((1 + m)/n)) - ((1/4 + I/4)*x*(e*x)^m*Erfi[((1/2 + I/2)*(1 + m - I*a*b*d^2*n*Pi - I*b^2*d^2*n*Pi*Log[c*x^n]))/(b*d*n*Sqrt[Pi])])/(E^(((I/2)*(1 + m)*(1 + m - (2*I)*a*b*d^2*n*Pi))/(b^2*d^2*n^2*Pi))*(1 + m)*(c*x^n)^((1 + m)/n)) + ((e*x)^(1 + m)*FresnelC[d*(a + b*Log[c*x^n])])/(e*(1 + m))","A",16,10,19,0.5263,1,"{6472, 4618, 2278, 2274, 15, 20, 2276, 2234, 2204, 2205}"
170,1,64,0,0.0693593,"\int e^{c+\frac{1}{2} i b^2 \pi  x^2} \text{FresnelC}(b x) \, dx","Int[E^(c + (I/2)*b^2*Pi*x^2)*FresnelC[b*x],x]","\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}","\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,"((-I/8)*E^c*Erfi[(1/2 + I/2)*b*Sqrt[Pi]*x]^2)/b + (b*E^c*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (I/2)*b^2*Pi*x^2])/4","A",4,4,22,0.1818,1,"{6437, 6376, 6375, 30}"
171,1,64,0,0.0662754,"\int e^{c-\frac{1}{2} i b^2 \pi  x^2} \text{FresnelC}(b x) \, dx","Int[E^(c - (I/2)*b^2*Pi*x^2)*FresnelC[b*x],x]","\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}","\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,"((-I/8)*E^c*Erf[(1/2 + I/2)*b*Sqrt[Pi]*x]^2)/b + (b*E^c*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (-I/2)*b^2*Pi*x^2])/4","A",4,4,22,0.1818,1,"{6437, 6373, 30, 6378}"
172,1,101,0,0.050629,"\int \text{FresnelC}(b x) \sin \left(c+\frac{1}{2} b^2 \pi  x^2\right) \, dx","Int[FresnelC[b*x]*Sin[c + (b^2*Pi*x^2)/2],x]","\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) \text{FresnelC}(b x) S(b x)}{2 b}+\frac{\sin (c) \text{FresnelC}(b x)^2}{2 b}","\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) \text{FresnelC}(b x) S(b x)}{2 b}+\frac{\sin (c) \text{FresnelC}(b x)^2}{2 b}",1,"(Cos[c]*FresnelC[b*x]*FresnelS[b*x])/(2*b) + (I/8)*b*x^2*Cos[c]*HypergeometricPFQ[{1, 1}, {3/2, 2}, (-I/2)*b^2*Pi*x^2] - (I/8)*b*x^2*Cos[c]*HypergeometricPFQ[{1, 1}, {3/2, 2}, (I/2)*b^2*Pi*x^2] + (FresnelC[b*x]^2*Sin[c])/(2*b)","A",4,4,19,0.2105,1,"{6449, 6441, 30, 6447}"
173,1,101,0,0.0478725,"\int \cos \left(c+\frac{1}{2} b^2 \pi  x^2\right) \text{FresnelC}(b x) \, dx","Int[Cos[c + (b^2*Pi*x^2)/2]*FresnelC[b*x],x]","-\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) \text{FresnelC}(b x) S(b x)}{2 b}+\frac{\cos (c) \text{FresnelC}(b x)^2}{2 b}","-\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) \text{FresnelC}(b x) S(b x)}{2 b}+\frac{\cos (c) \text{FresnelC}(b x)^2}{2 b}",1,"(Cos[c]*FresnelC[b*x]^2)/(2*b) - (FresnelC[b*x]*FresnelS[b*x]*Sin[c])/(2*b) - (I/8)*b*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (-I/2)*b^2*Pi*x^2]*Sin[c] + (I/8)*b*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (I/2)*b^2*Pi*x^2]*Sin[c]","A",4,4,19,0.2105,1,"{6443, 6441, 30, 6447}"
174,1,13,0,0.0148672,"\int \cos \left(\frac{1}{2} b^2 \pi  x^2\right) \text{FresnelC}(b x)^2 \, dx","Int[Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x]^2,x]","\frac{\text{FresnelC}(b x)^3}{3 b}","\frac{\text{FresnelC}(b x)^3}{3 b}",1,"FresnelC[b*x]^3/(3*b)","A",2,2,19,0.1053,1,"{6441, 30}"
175,1,13,0,0.0116175,"\int \cos \left(\frac{1}{2} b^2 \pi  x^2\right) \text{FresnelC}(b x) \, dx","Int[Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x],x]","\frac{\text{FresnelC}(b x)^2}{2 b}","\frac{\text{FresnelC}(b x)^2}{2 b}",1,"FresnelC[b*x]^2/(2*b)","A",2,2,17,0.1176,1,"{6441, 30}"
176,1,9,0,0.0155068,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right)}{\text{FresnelC}(b x)} \, dx","Int[Cos[(b^2*Pi*x^2)/2]/FresnelC[b*x],x]","\frac{\log (\text{FresnelC}(b x))}{b}","\frac{\log (\text{FresnelC}(b x))}{b}",1,"Log[FresnelC[b*x]]/b","A",2,2,19,0.1053,1,"{6441, 29}"
177,1,11,0,0.0149059,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right)}{\text{FresnelC}(b x)^2} \, dx","Int[Cos[(b^2*Pi*x^2)/2]/FresnelC[b*x]^2,x]","-\frac{1}{b \text{FresnelC}(b x)}","-\frac{1}{b \text{FresnelC}(b x)}",1,"-(1/(b*FresnelC[b*x]))","A",2,2,19,0.1053,1,"{6441, 30}"
178,1,13,0,0.0156124,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right)}{\text{FresnelC}(b x)^3} \, dx","Int[Cos[(b^2*Pi*x^2)/2]/FresnelC[b*x]^3,x]","-\frac{1}{2 b \text{FresnelC}(b x)^2}","-\frac{1}{2 b \text{FresnelC}(b x)^2}",1,"-1/(2*b*FresnelC[b*x]^2)","A",2,2,19,0.1053,1,"{6441, 30}"
179,1,17,0,0.0187874,"\int \cos \left(\frac{1}{2} b^2 \pi  x^2\right) \text{FresnelC}(b x)^n \, dx","Int[Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x]^n,x]","\frac{\text{FresnelC}(b x)^{n+1}}{b (n+1)}","\frac{\text{FresnelC}(b x)^{n+1}}{b (n+1)}",1,"FresnelC[b*x]^(1 + n)/(b*(1 + n))","A",2,2,19,0.1053,1,"{6441, 30}"
180,1,231,0,0.3829075,"\int x^8 \cos \left(\frac{1}{2} b^2 \pi  x^2\right) \text{FresnelC}(b x) \, dx","Int[x^8*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x],x]","\frac{x^7 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{35 x^3 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}+\frac{7 x^5 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{105 x \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^4 b^8}+\frac{105 \text{FresnelC}(b x)^2}{2 \pi ^4 b^9}-\frac{7 x^6}{12 \pi ^2 b^3}+\frac{105 x^2}{4 \pi ^4 b^7}-\frac{5 x^4 \sin \left(\pi  b^2 x^2\right)}{2 \pi ^3 b^5}+\frac{40 \sin \left(\pi  b^2 x^2\right)}{\pi ^5 b^9}+\frac{x^6 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}-\frac{55 x^2 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^4 b^7}","\frac{x^7 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{35 x^3 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}+\frac{7 x^5 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{105 x \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^4 b^8}+\frac{105 \text{FresnelC}(b x)^2}{2 \pi ^4 b^9}-\frac{7 x^6}{12 \pi ^2 b^3}+\frac{105 x^2}{4 \pi ^4 b^7}-\frac{5 x^4 \sin \left(\pi  b^2 x^2\right)}{2 \pi ^3 b^5}+\frac{40 \sin \left(\pi  b^2 x^2\right)}{\pi ^5 b^9}+\frac{x^6 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}-\frac{55 x^2 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^4 b^7}",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",22,10,20,0.5000,1,"{6455, 6463, 6441, 30, 3380, 2634, 3379, 3296, 2637, 3309}"
181,1,215,0,0.259335,"\int x^7 \cos \left(\frac{1}{2} b^2 \pi  x^2\right) \text{FresnelC}(b x) \, dx","Int[x^7*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x],x]","\frac{x^6 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{24 x^2 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}+\frac{6 x^4 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{48 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^4 b^8}+\frac{531 \text{FresnelC}\left(\sqrt{2} b x\right)}{16 \sqrt{2} \pi ^4 b^8}-\frac{3 x^5}{5 \pi ^2 b^3}-\frac{17 x^3 \sin \left(\pi  b^2 x^2\right)}{8 \pi ^3 b^5}+\frac{x^5 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}-\frac{147 x \cos \left(\pi  b^2 x^2\right)}{16 \pi ^4 b^7}+\frac{24 x}{\pi ^4 b^7}","\frac{x^6 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{24 x^2 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}+\frac{6 x^4 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{48 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^4 b^8}+\frac{531 \text{FresnelC}\left(\sqrt{2} b x\right)}{16 \sqrt{2} \pi ^4 b^8}-\frac{3 x^5}{5 \pi ^2 b^3}-\frac{17 x^3 \sin \left(\pi  b^2 x^2\right)}{8 \pi ^3 b^5}+\frac{x^5 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}-\frac{147 x \cos \left(\pi  b^2 x^2\right)}{16 \pi ^4 b^7}+\frac{24 x}{\pi ^4 b^7}",1,"(24*x)/(b^7*Pi^4) - (3*x^5)/(5*b^3*Pi^2) - (147*x*Cos[b^2*Pi*x^2])/(16*b^7*Pi^4) + (x^5*Cos[b^2*Pi*x^2])/(4*b^3*Pi^2) - (48*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(b^8*Pi^4) + (6*x^4*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(b^4*Pi^2) + (531*FresnelC[Sqrt[2]*b*x])/(16*Sqrt[2]*b^8*Pi^4) - (24*x^2*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^6*Pi^3) + (x^6*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^2*Pi) - (17*x^3*Sin[b^2*Pi*x^2])/(8*b^5*Pi^3)","A",18,9,20,0.4500,1,"{6455, 6463, 6461, 3358, 3352, 3385, 3392, 30, 3386}"
182,1,247,0,0.2531599,"\int x^6 \cos \left(\frac{1}{2} b^2 \pi  x^2\right) \text{FresnelC}(b x) \, dx","Int[x^6*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x],x]","\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 \text{FresnelC}(b x) S(b x)}{2 \pi ^3 b^7}+\frac{x^5 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{15 x \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}+\frac{5 x^3 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{5 x^4}{8 \pi ^2 b^3}-\frac{7 x^2 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^3 b^5}+\frac{x^4 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}-\frac{11 \cos \left(\pi  b^2 x^2\right)}{2 \pi ^4 b^7}","\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 \text{FresnelC}(b x) S(b x)}{2 \pi ^3 b^7}+\frac{x^5 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{15 x \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}+\frac{5 x^3 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{5 x^4}{8 \pi ^2 b^3}-\frac{7 x^2 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^3 b^5}+\frac{x^4 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}-\frac{11 \cos \left(\pi  b^2 x^2\right)}{2 \pi ^4 b^7}",1,"(-5*x^4)/(8*b^3*Pi^2) - (11*Cos[b^2*Pi*x^2])/(2*b^7*Pi^4) + (x^4*Cos[b^2*Pi*x^2])/(4*b^3*Pi^2) + (5*x^3*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(b^4*Pi^2) + (15*FresnelC[b*x]*FresnelS[b*x])/(2*b^7*Pi^3) + (((15*I)/8)*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (-I/2)*b^2*Pi*x^2])/(b^5*Pi^3) - (((15*I)/8)*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (I/2)*b^2*Pi*x^2])/(b^5*Pi^3) - (15*x*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^6*Pi^3) + (x^5*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^2*Pi) - (7*x^2*Sin[b^2*Pi*x^2])/(4*b^5*Pi^3)","A",15,9,20,0.4500,1,"{6455, 6463, 6447, 3379, 2638, 3380, 3309, 30, 3296}"
183,1,157,0,0.1510982,"\int x^5 \cos \left(\frac{1}{2} b^2 \pi  x^2\right) \text{FresnelC}(b x) \, dx","Int[x^5*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x],x]","\frac{x^4 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{8 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}+\frac{4 x^2 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}+\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{11 x \sin \left(\pi  b^2 x^2\right)}{8 \pi ^3 b^5}+\frac{x^3 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}","\frac{x^4 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{8 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}+\frac{4 x^2 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}+\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{11 x \sin \left(\pi  b^2 x^2\right)}{8 \pi ^3 b^5}+\frac{x^3 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}",1,"(-2*x^3)/(3*b^3*Pi^2) + (x^3*Cos[b^2*Pi*x^2])/(4*b^3*Pi^2) + (4*x^2*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(b^4*Pi^2) + (43*FresnelS[Sqrt[2]*b*x])/(8*Sqrt[2]*b^6*Pi^3) - (8*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^6*Pi^3) + (x^4*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^2*Pi) - (11*x*Sin[b^2*Pi*x^2])/(8*b^5*Pi^3)","A",11,8,20,0.4000,1,"{6455, 6463, 6453, 3351, 3392, 30, 3386, 3385}"
184,1,120,0,0.1181082,"\int x^4 \cos \left(\frac{1}{2} b^2 \pi  x^2\right) \text{FresnelC}(b x) \, dx","Int[x^4*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x],x]","\frac{x^3 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{3 x \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{3 \text{FresnelC}(b x)^2}{2 \pi ^2 b^5}-\frac{3 x^2}{4 \pi ^2 b^3}-\frac{\sin \left(\pi  b^2 x^2\right)}{\pi ^3 b^5}+\frac{x^2 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}","\frac{x^3 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{3 x \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{3 \text{FresnelC}(b x)^2}{2 \pi ^2 b^5}-\frac{3 x^2}{4 \pi ^2 b^3}-\frac{\sin \left(\pi  b^2 x^2\right)}{\pi ^3 b^5}+\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",9,9,20,0.4500,1,"{6455, 6463, 6441, 30, 3380, 2634, 3379, 3296, 2637}"
185,1,104,0,0.0782079,"\int x^3 \cos \left(\frac{1}{2} b^2 \pi  x^2\right) \text{FresnelC}(b x) \, dx","Int[x^3*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x],x]","\frac{x^2 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{2 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{5 \text{FresnelC}\left(\sqrt{2} b x\right)}{4 \sqrt{2} \pi ^2 b^4}+\frac{x \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}-\frac{x}{\pi ^2 b^3}","\frac{x^2 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{2 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{5 \text{FresnelC}\left(\sqrt{2} b x\right)}{4 \sqrt{2} \pi ^2 b^4}+\frac{x \cos \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}-\frac{x}{\pi ^2 b^3}",1,"-(x/(b^3*Pi^2)) + (x*Cos[b^2*Pi*x^2])/(4*b^3*Pi^2) + (2*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(b^4*Pi^2) - (5*FresnelC[Sqrt[2]*b*x])/(4*Sqrt[2]*b^4*Pi^2) + (x^2*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^2*Pi)","A",7,5,20,0.2500,1,"{6455, 6461, 3358, 3352, 3385}"
186,1,136,0,0.0595254,"\int x^2 \cos \left(\frac{1}{2} b^2 \pi  x^2\right) \text{FresnelC}(b x) \, dx","Int[x^2*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x],x]","-\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{\text{FresnelC}(b x) S(b x)}{2 \pi  b^3}+\frac{x \text{FresnelC}(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}","-\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{\text{FresnelC}(b x) S(b x)}{2 \pi  b^3}+\frac{x \text{FresnelC}(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,"Cos[b^2*Pi*x^2]/(4*b^3*Pi^2) - (FresnelC[b*x]*FresnelS[b*x])/(2*b^3*Pi) - ((I/8)*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (-I/2)*b^2*Pi*x^2])/(b*Pi) + ((I/8)*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (I/2)*b^2*Pi*x^2])/(b*Pi) + (x*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^2*Pi)","A",4,4,20,0.2000,1,"{6455, 6447, 3379, 2638}"
187,1,48,0,0.0208259,"\int x \cos \left(\frac{1}{2} b^2 \pi  x^2\right) \text{FresnelC}(b x) \, dx","Int[x*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x],x]","\frac{\text{FresnelC}(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}","\frac{\text{FresnelC}(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,"-FresnelS[Sqrt[2]*b*x]/(2*Sqrt[2]*b^2*Pi) + (FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^2*Pi)","A",2,2,18,0.1111,1,"{6453, 3351}"
188,1,13,0,0.0114821,"\int \cos \left(\frac{1}{2} b^2 \pi  x^2\right) \text{FresnelC}(b x) \, dx","Int[Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x],x]","\frac{\text{FresnelC}(b x)^2}{2 b}","\frac{\text{FresnelC}(b x)^2}{2 b}",1,"FresnelC[b*x]^2/(2*b)","A",2,2,17,0.1176,1,"{6441, 30}"
189,0,0,0,0.0168393,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) \text{FresnelC}(b x)}{x} \, dx","Int[(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) \text{FresnelC}(b x)}{x} \, dx","\text{Int}\left(\frac{\text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)",0,"Defer[Int][(Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/x, x]","A",0,0,0,0,-1,"{}"
190,0,0,0,0.0187246,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) \text{FresnelC}(b x)}{x^2} \, dx","Int[(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) \text{FresnelC}(b x)}{x^2} \, dx","\text{Int}\left(\frac{\text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x^2},x\right)",0,"Defer[Int][(Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/x^2, x]","A",0,0,0,0,-1,"{}"
191,0,0,0,0.0564858,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) \text{FresnelC}(b x)}{x^3} \, dx","Int[(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) \text{FresnelC}(b x)}{x^3} \, dx","-\frac{1}{2} \pi  b^2 \text{Int}\left(\frac{\text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)-\frac{\text{FresnelC}(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,"-b/(4*x) - (b*Cos[b^2*Pi*x^2])/(4*x) - (Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(2*x^2) - (b^2*Pi*FresnelS[Sqrt[2]*b*x])/(2*Sqrt[2]) - (b^2*Pi*Defer[Int][(FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/x, x])/2","A",0,0,0,0,-1,"{}"
192,1,109,0,0.1151578,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) \text{FresnelC}(b x)}{x^4} \, dx","Int[(Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/x^4,x]","\frac{\pi  b^2 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 x}-\frac{\text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 x^3}-\frac{1}{6} \pi ^2 b^3 \text{FresnelC}(b x)^2-\frac{1}{6} \pi  b^3 \text{Si}\left(b^2 \pi  x^2\right)-\frac{b \cos \left(\pi  b^2 x^2\right)}{12 x^2}-\frac{b}{12 x^2}","\frac{\pi  b^2 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 x}-\frac{\text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{3 x^3}-\frac{1}{6} \pi ^2 b^3 \text{FresnelC}(b x)^2-\frac{1}{6} \pi  b^3 \text{Si}\left(b^2 \pi  x^2\right)-\frac{b \cos \left(\pi  b^2 x^2\right)}{12 x^2}-\frac{b}{12 x^2}",1,"-b/(12*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",8,8,20,0.4000,1,"{6457, 6465, 6441, 30, 3375, 3380, 3297, 3299}"
193,0,0,0,0.1153493,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) \text{FresnelC}(b x)}{x^5} \, dx","Int[(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) \text{FresnelC}(b x)}{x^5} \, dx","-\frac{1}{8} \pi ^2 b^4 \text{Int}\left(\frac{\text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)+\frac{\pi  b^2 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{8 x^2}-\frac{\text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 x^4}-\frac{7 \pi ^2 b^4 \text{FresnelC}\left(\sqrt{2} b x\right)}{24 \sqrt{2}}+\frac{7 \pi  b^3 \sin \left(\pi  b^2 x^2\right)}{48 x}-\frac{b \cos \left(\pi  b^2 x^2\right)}{24 x^3}-\frac{b}{24 x^3}",0,"-b/(24*x^3) - (b*Cos[b^2*Pi*x^2])/(24*x^3) - (Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(4*x^4) - (7*b^4*Pi^2*FresnelC[Sqrt[2]*b*x])/(24*Sqrt[2]) + (b^2*Pi*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(8*x^2) + (7*b^3*Pi*Sin[b^2*Pi*x^2])/(48*x) - (b^4*Pi^2*Defer[Int][(Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/x, x])/8","A",0,0,0,0,-1,"{}"
194,0,0,0,0.1923158,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) \text{FresnelC}(b x)}{x^6} \, dx","Int[(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) \text{FresnelC}(b x)}{x^6} \, dx","-\frac{1}{15} \pi ^2 b^4 \text{Int}\left(\frac{\text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x^2},x\right)-\frac{1}{24} \pi ^2 b^5 \text{CosIntegral}\left(\pi  b^2 x^2\right)+\frac{\pi  b^2 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{15 x^3}-\frac{\text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 x^5}+\frac{\pi  b^3 \sin \left(\pi  b^2 x^2\right)}{24 x^2}-\frac{b \cos \left(\pi  b^2 x^2\right)}{40 x^4}-\frac{b}{40 x^4}",0,"-b/(40*x^4) - (b*Cos[b^2*Pi*x^2])/(40*x^4) - (b^5*Pi^2*CosIntegral[b^2*Pi*x^2])/24 - (Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(5*x^5) + (b^2*Pi*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(15*x^3) + (b^3*Pi*Sin[b^2*Pi*x^2])/(24*x^2) - (b^4*Pi^2*Defer[Int][(Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/x^2, x])/15","A",0,0,0,0,-1,"{}"
195,0,0,0,0.2037196,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) \text{FresnelC}(b x)}{x^7} \, dx","Int[(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) \text{FresnelC}(b x)}{x^7} \, dx","\frac{1}{48} \pi ^3 b^6 \text{Int}\left(\frac{\text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)+\frac{\pi  b^2 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{24 x^4}+\frac{\pi ^2 b^4 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{48 x^2}-\frac{\text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 x^6}+\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{13 \pi  b^3 \sin \left(\pi  b^2 x^2\right)}{720 x^3}+\frac{67 \pi ^2 b^5 \cos \left(\pi  b^2 x^2\right)}{1440 x}-\frac{b \cos \left(\pi  b^2 x^2\right)}{60 x^5}+\frac{\pi ^2 b^5}{96 x}-\frac{b}{60 x^5}",0,"-b/(60*x^5) + (b^5*Pi^2)/(96*x) - (b*Cos[b^2*Pi*x^2])/(60*x^5) + (67*b^5*Pi^2*Cos[b^2*Pi*x^2])/(1440*x) - (Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(6*x^6) + (b^4*Pi^2*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(48*x^2) + (7*b^6*Pi^3*FresnelS[Sqrt[2]*b*x])/(144*Sqrt[2]) + (Sqrt[2]*b^6*Pi^3*FresnelS[Sqrt[2]*b*x])/45 + (b^2*Pi*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(24*x^4) + (13*b^3*Pi*Sin[b^2*Pi*x^2])/(720*x^3) + (b^6*Pi^3*Defer[Int][(FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/x, x])/48","A",0,0,0,0,-1,"{}"
196,1,224,0,0.3515946,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) \text{FresnelC}(b x)}{x^8} \, dx","Int[(Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/x^8,x]","-\frac{\pi ^3 b^6 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{105 x}+\frac{\pi  b^2 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{35 x^5}+\frac{\pi ^2 b^4 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{105 x^3}-\frac{\text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 x^7}+\frac{1}{210} \pi ^4 b^7 \text{FresnelC}(b x)^2+\frac{1}{70} \pi ^3 b^7 \text{Si}\left(b^2 \pi  x^2\right)+\frac{\pi ^2 b^5}{420 x^2}+\frac{\pi  b^3 \sin \left(\pi  b^2 x^2\right)}{105 x^4}+\frac{\pi ^2 b^5 \cos \left(\pi  b^2 x^2\right)}{84 x^2}-\frac{b \cos \left(\pi  b^2 x^2\right)}{84 x^6}-\frac{b}{84 x^6}","-\frac{\pi ^3 b^6 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{105 x}+\frac{\pi  b^2 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{35 x^5}+\frac{\pi ^2 b^4 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{105 x^3}-\frac{\text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 x^7}+\frac{1}{210} \pi ^4 b^7 \text{FresnelC}(b x)^2+\frac{1}{70} \pi ^3 b^7 \text{Si}\left(b^2 \pi  x^2\right)+\frac{\pi ^2 b^5}{420 x^2}+\frac{\pi  b^3 \sin \left(\pi  b^2 x^2\right)}{105 x^4}+\frac{\pi ^2 b^5 \cos \left(\pi  b^2 x^2\right)}{84 x^2}-\frac{b \cos \left(\pi  b^2 x^2\right)}{84 x^6}-\frac{b}{84 x^6}",1,"-b/(84*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",19,9,20,0.4500,1,"{6457, 6465, 6441, 30, 3375, 3380, 3297, 3299, 3379}"
197,0,0,0,0.3038013,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) \text{FresnelC}(b x)}{x^9} \, dx","Int[(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) \text{FresnelC}(b x)}{x^9} \, dx","\frac{1}{384} \pi ^4 b^8 \text{Int}\left(\frac{\text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)-\frac{\pi ^3 b^6 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{384 x^2}+\frac{\pi  b^2 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{48 x^6}+\frac{\pi ^2 b^4 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{192 x^4}-\frac{\text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{8 x^8}+\frac{853 \pi ^4 b^8 \text{FresnelC}\left(\sqrt{2} b x\right)}{40320 \sqrt{2}}+\frac{\pi ^2 b^5}{1152 x^3}-\frac{853 \pi ^3 b^7 \sin \left(\pi  b^2 x^2\right)}{80640 x}+\frac{19 \pi  b^3 \sin \left(\pi  b^2 x^2\right)}{3360 x^5}+\frac{187 \pi ^2 b^5 \cos \left(\pi  b^2 x^2\right)}{40320 x^3}-\frac{b \cos \left(\pi  b^2 x^2\right)}{112 x^7}-\frac{b}{112 x^7}",0,"-b/(112*x^7) + (b^5*Pi^2)/(1152*x^3) - (b*Cos[b^2*Pi*x^2])/(112*x^7) + (187*b^5*Pi^2*Cos[b^2*Pi*x^2])/(40320*x^3) - (Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(8*x^8) + (b^4*Pi^2*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(192*x^4) + (853*b^8*Pi^4*FresnelC[Sqrt[2]*b*x])/(40320*Sqrt[2]) + (b^2*Pi*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(48*x^6) - (b^6*Pi^3*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(384*x^2) + (19*b^3*Pi*Sin[b^2*Pi*x^2])/(3360*x^5) - (853*b^7*Pi^3*Sin[b^2*Pi*x^2])/(80640*x) + (b^8*Pi^4*Defer[Int][(Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/x, x])/384","A",0,0,0,0,-1,"{}"
198,0,0,0,0.4951356,"\int \frac{\cos \left(\frac{1}{2} b^2 \pi  x^2\right) \text{FresnelC}(b x)}{x^{10}} \, dx","Int[(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) \text{FresnelC}(b x)}{x^{10}} \, dx","\frac{1}{945} \pi ^4 b^8 \text{Int}\left(\frac{\text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x^2},x\right)+\frac{5 \pi ^4 b^9 \text{CosIntegral}\left(\pi  b^2 x^2\right)}{2016}-\frac{\pi ^3 b^6 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{945 x^3}+\frac{\pi  b^2 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{63 x^7}+\frac{\pi ^2 b^4 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{315 x^5}-\frac{\text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{9 x^9}+\frac{\pi ^2 b^5}{2520 x^4}-\frac{5 \pi ^3 b^7 \sin \left(\pi  b^2 x^2\right)}{2016 x^2}+\frac{11 \pi  b^3 \sin \left(\pi  b^2 x^2\right)}{3024 x^6}+\frac{67 \pi ^2 b^5 \cos \left(\pi  b^2 x^2\right)}{30240 x^4}-\frac{b \cos \left(\pi  b^2 x^2\right)}{144 x^8}-\frac{b}{144 x^8}",0,"-b/(144*x^8) + (b^5*Pi^2)/(2520*x^4) - (b*Cos[b^2*Pi*x^2])/(144*x^8) + (67*b^5*Pi^2*Cos[b^2*Pi*x^2])/(30240*x^4) + (5*b^9*Pi^4*CosIntegral[b^2*Pi*x^2])/2016 - (Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(9*x^9) + (b^4*Pi^2*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(315*x^5) + (b^2*Pi*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(63*x^7) - (b^6*Pi^3*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(945*x^3) + (11*b^3*Pi*Sin[b^2*Pi*x^2])/(3024*x^6) - (5*b^7*Pi^3*Sin[b^2*Pi*x^2])/(2016*x^2) + (b^8*Pi^4*Defer[Int][(Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/x^2, x])/945","A",0,0,0,0,-1,"{}"
199,0,0,0,0.0129616,"\int \text{FresnelC}(b x)^n \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Int[FresnelC[b*x]^n*Sin[(b^2*Pi*x^2)/2],x]","\int \text{FresnelC}(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) \text{FresnelC}(b x)^n,x\right)",0,"Defer[Int][FresnelC[b*x]^n*Sin[(b^2*Pi*x^2)/2], x]","A",0,0,0,0,-1,"{}"
200,1,308,0,0.43063,"\int x^8 \text{FresnelC}(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Int[x^8*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2],x]","\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 \text{FresnelC}(b x) S(b x)}{2 \pi ^4 b^9}+\frac{7 x^5 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{105 x \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^4 b^8}-\frac{x^7 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{35 x^3 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}-\frac{35 x^4}{8 \pi ^3 b^5}+\frac{x^6 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}-\frac{55 x^2 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^4 b^7}+\frac{5 x^4 \cos \left(\pi  b^2 x^2\right)}{2 \pi ^3 b^5}-\frac{40 \cos \left(\pi  b^2 x^2\right)}{\pi ^5 b^9}+\frac{x^8}{16 \pi  b}","\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 \text{FresnelC}(b x) S(b x)}{2 \pi ^4 b^9}+\frac{7 x^5 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{105 x \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^4 b^8}-\frac{x^7 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{35 x^3 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}-\frac{35 x^4}{8 \pi ^3 b^5}+\frac{x^6 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}-\frac{55 x^2 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^4 b^7}+\frac{5 x^4 \cos \left(\pi  b^2 x^2\right)}{2 \pi ^3 b^5}-\frac{40 \cos \left(\pi  b^2 x^2\right)}{\pi ^5 b^9}+\frac{x^8}{16 \pi  b}",1,"(-35*x^4)/(8*b^5*Pi^3) + x^8/(16*b*Pi) - (40*Cos[b^2*Pi*x^2])/(b^9*Pi^5) + (5*x^4*Cos[b^2*Pi*x^2])/(2*b^5*Pi^3) + (35*x^3*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(b^6*Pi^3) - (x^7*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(b^2*Pi) + (105*FresnelC[b*x]*FresnelS[b*x])/(2*b^9*Pi^4) + (((105*I)/8)*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (-I/2)*b^2*Pi*x^2])/(b^7*Pi^4) - (((105*I)/8)*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (I/2)*b^2*Pi*x^2])/(b^7*Pi^4) - (105*x*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^8*Pi^4) + (7*x^5*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^4*Pi^2) - (55*x^2*Sin[b^2*Pi*x^2])/(4*b^7*Pi^4) + (x^6*Sin[b^2*Pi*x^2])/(4*b^3*Pi^2)","A",23,9,20,0.4500,1,"{6463, 6455, 6447, 3379, 2638, 3380, 3309, 30, 3296}"
201,1,218,0,0.2708803,"\int x^7 \text{FresnelC}(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Int[x^7*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2],x]","\frac{6 x^4 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{48 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^4 b^8}-\frac{x^6 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{24 x^2 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}+\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^5 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}-\frac{147 x \sin \left(\pi  b^2 x^2\right)}{16 \pi ^4 b^7}+\frac{17 x^3 \cos \left(\pi  b^2 x^2\right)}{8 \pi ^3 b^5}+\frac{x^7}{14 \pi  b}","\frac{6 x^4 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{48 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^4 b^8}-\frac{x^6 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{24 x^2 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}+\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^5 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}-\frac{147 x \sin \left(\pi  b^2 x^2\right)}{16 \pi ^4 b^7}+\frac{17 x^3 \cos \left(\pi  b^2 x^2\right)}{8 \pi ^3 b^5}+\frac{x^7}{14 \pi  b}",1,"(-4*x^3)/(b^5*Pi^3) + x^7/(14*b*Pi) + (17*x^3*Cos[b^2*Pi*x^2])/(8*b^5*Pi^3) + (24*x^2*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(b^6*Pi^3) - (x^6*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(b^2*Pi) + (531*FresnelS[Sqrt[2]*b*x])/(16*Sqrt[2]*b^8*Pi^4) - (48*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^8*Pi^4) + (6*x^4*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^4*Pi^2) - (147*x*Sin[b^2*Pi*x^2])/(16*b^7*Pi^4) + (x^5*Sin[b^2*Pi*x^2])/(4*b^3*Pi^2)","A",18,8,20,0.4000,1,"{6463, 6455, 6453, 3351, 3392, 30, 3386, 3385}"
202,1,185,0,0.254223,"\int x^6 \text{FresnelC}(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Int[x^6*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2],x]","\frac{5 x^3 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{x^5 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{15 x \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}-\frac{15 \text{FresnelC}(b x)^2}{2 \pi ^3 b^7}-\frac{15 x^2}{4 \pi ^3 b^5}+\frac{x^4 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}-\frac{11 \sin \left(\pi  b^2 x^2\right)}{2 \pi ^4 b^7}+\frac{7 x^2 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^3 b^5}+\frac{x^6}{12 \pi  b}","\frac{5 x^3 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{x^5 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{15 x \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}-\frac{15 \text{FresnelC}(b x)^2}{2 \pi ^3 b^7}-\frac{15 x^2}{4 \pi ^3 b^5}+\frac{x^4 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}-\frac{11 \sin \left(\pi  b^2 x^2\right)}{2 \pi ^4 b^7}+\frac{7 x^2 \cos \left(\pi  b^2 x^2\right)}{4 \pi ^3 b^5}+\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",16,10,20,0.5000,1,"{6463, 6455, 6441, 30, 3380, 2634, 3379, 3296, 2637, 3309}"
203,1,167,0,0.1743745,"\int x^5 \text{FresnelC}(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Int[x^5*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2],x]","\frac{4 x^2 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{x^4 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{8 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}-\frac{43 \text{FresnelC}\left(\sqrt{2} b x\right)}{8 \sqrt{2} \pi ^3 b^6}+\frac{x^3 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}+\frac{11 x \cos \left(\pi  b^2 x^2\right)}{8 \pi ^3 b^5}-\frac{4 x}{\pi ^3 b^5}+\frac{x^5}{10 \pi  b}","\frac{4 x^2 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{x^4 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{8 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^3 b^6}-\frac{43 \text{FresnelC}\left(\sqrt{2} b x\right)}{8 \sqrt{2} \pi ^3 b^6}+\frac{x^3 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}+\frac{11 x \cos \left(\pi  b^2 x^2\right)}{8 \pi ^3 b^5}-\frac{4 x}{\pi ^3 b^5}+\frac{x^5}{10 \pi  b}",1,"(-4*x)/(b^5*Pi^3) + x^5/(10*b*Pi) + (11*x*Cos[b^2*Pi*x^2])/(8*b^5*Pi^3) + (8*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(b^6*Pi^3) - (x^4*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(b^2*Pi) - (43*FresnelC[Sqrt[2]*b*x])/(8*Sqrt[2]*b^6*Pi^3) + (4*x^2*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^4*Pi^2) + (x^3*Sin[b^2*Pi*x^2])/(4*b^3*Pi^2)","A",13,9,20,0.4500,1,"{6463, 6455, 6461, 3358, 3352, 3385, 3392, 30, 3386}"
204,1,196,0,0.1568099,"\int x^4 \text{FresnelC}(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Int[x^4*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2],x]","-\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 \text{FresnelC}(b x) S(b x)}{2 \pi ^2 b^5}+\frac{3 x \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{x^3 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{x^2 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}+\frac{\cos \left(\pi  b^2 x^2\right)}{\pi ^3 b^5}+\frac{x^4}{8 \pi  b}","-\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 \text{FresnelC}(b x) S(b x)}{2 \pi ^2 b^5}+\frac{3 x \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{x^3 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{x^2 \sin \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}+\frac{\cos \left(\pi  b^2 x^2\right)}{\pi ^3 b^5}+\frac{x^4}{8 \pi  b}",1,"x^4/(8*b*Pi) + Cos[b^2*Pi*x^2]/(b^5*Pi^3) - (x^3*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(b^2*Pi) - (3*FresnelC[b*x]*FresnelS[b*x])/(2*b^5*Pi^2) - (((3*I)/8)*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (-I/2)*b^2*Pi*x^2])/(b^3*Pi^2) + (((3*I)/8)*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (I/2)*b^2*Pi*x^2])/(b^3*Pi^2) + (3*x*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^4*Pi^2) + (x^2*Sin[b^2*Pi*x^2])/(4*b^3*Pi^2)","A",10,9,20,0.4500,1,"{6463, 6455, 6447, 3379, 2638, 3380, 3309, 30, 3296}"
205,1,109,0,0.0893288,"\int x^3 \text{FresnelC}(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Int[x^3*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2],x]","\frac{2 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{x^2 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{5 S\left(\sqrt{2} b x\right)}{4 \sqrt{2} \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}","\frac{2 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi ^2 b^4}-\frac{x^2 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}-\frac{5 S\left(\sqrt{2} b x\right)}{4 \sqrt{2} \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,"x^3/(6*b*Pi) - (x^2*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(b^2*Pi) - (5*FresnelS[Sqrt[2]*b*x])/(4*Sqrt[2]*b^4*Pi^2) + (2*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(b^4*Pi^2) + (x*Sin[b^2*Pi*x^2])/(4*b^3*Pi^2)","A",7,6,20,0.3000,1,"{6463, 6453, 3351, 3392, 30, 3386}"
206,1,74,0,0.0570508,"\int x^2 \text{FresnelC}(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Int[x^2*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2],x]","-\frac{x \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{\text{FresnelC}(b x)^2}{2 \pi  b^3}+\frac{\sin \left(\pi  b^2 x^2\right)}{4 \pi ^2 b^3}+\frac{x^2}{4 \pi  b}","-\frac{x \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{\text{FresnelC}(b x)^2}{2 \pi  b^3}+\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",5,5,20,0.2500,1,"{6463, 6441, 30, 3380, 2634}"
207,1,60,0,0.0317032,"\int x \text{FresnelC}(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Int[x*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2],x]","-\frac{\text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{\text{FresnelC}\left(\sqrt{2} b x\right)}{2 \sqrt{2} \pi  b^2}+\frac{x}{2 \pi  b}","-\frac{\text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{\pi  b^2}+\frac{\text{FresnelC}\left(\sqrt{2} b x\right)}{2 \sqrt{2} \pi  b^2}+\frac{x}{2 \pi  b}",1,"x/(2*b*Pi) - (Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(b^2*Pi) + FresnelC[Sqrt[2]*b*x]/(2*Sqrt[2]*b^2*Pi)","A",4,3,18,0.1667,1,"{6461, 3358, 3352}"
208,1,80,0,0.0157251,"\int \text{FresnelC}(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right) \, dx","Int[FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2],x]","\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{\text{FresnelC}(b x) S(b x)}{2 b}","\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{\text{FresnelC}(b x) S(b x)}{2 b}",1,"(FresnelC[b*x]*FresnelS[b*x])/(2*b) + (I/8)*b*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (-I/2)*b^2*Pi*x^2] - (I/8)*b*x^2*HypergeometricPFQ[{1, 1}, {3/2, 2}, (I/2)*b^2*Pi*x^2]","A",1,1,17,0.05882,1,"{6447}"
209,0,0,0,0.0172122,"\int \frac{\text{FresnelC}(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x} \, dx","Int[(FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/x,x]","\int \frac{\text{FresnelC}(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x} \, dx","\text{Int}\left(\frac{\text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)",0,"Defer[Int][(FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/x, x]","A",0,0,0,0,-1,"{}"
210,1,48,0,0.0427923,"\int \frac{\text{FresnelC}(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^2} \, dx","Int[(FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/x^2,x]","-\frac{\text{FresnelC}(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 \text{FresnelC}(b x)^2","-\frac{\text{FresnelC}(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 \text{FresnelC}(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",4,4,20,0.2000,1,"{6465, 6441, 30, 3375}"
211,0,0,0,0.0563796,"\int \frac{\text{FresnelC}(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^3} \, dx","Int[(FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/x^3,x]","\int \frac{\text{FresnelC}(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{\text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)-\frac{\text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{2 x^2}+\frac{\pi  b^2 \text{FresnelC}\left(\sqrt{2} b x\right)}{2 \sqrt{2}}-\frac{b \sin \left(\pi  b^2 x^2\right)}{4 x}",0,"(b^2*Pi*FresnelC[Sqrt[2]*b*x])/(2*Sqrt[2]) - (FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(2*x^2) - (b*Sin[b^2*Pi*x^2])/(4*x) + (b^2*Pi*Defer[Int][(Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/x, x])/2","A",0,0,0,0,-1,"{}"
212,0,0,0,0.0893682,"\int \frac{\text{FresnelC}(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^4} \, dx","Int[(FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/x^4,x]","\int \frac{\text{FresnelC}(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{\text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x^2},x\right)+\frac{1}{12} \pi  b^3 \text{CosIntegral}\left(\pi  b^2 x^2\right)-\frac{\text{FresnelC}(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}",0,"(b^3*Pi*CosIntegral[b^2*Pi*x^2])/12 - (FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(3*x^3) - (b*Sin[b^2*Pi*x^2])/(12*x^2) + (b^2*Pi*Defer[Int][(Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/x^2, x])/3","A",0,0,0,0,-1,"{}"
213,0,0,0,0.1190521,"\int \frac{\text{FresnelC}(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^5} \, dx","Int[(FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/x^5,x]","\int \frac{\text{FresnelC}(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{\text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)-\frac{\text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{4 x^4}-\frac{\pi  b^2 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{8 x^2}-\frac{7 \pi ^2 b^4 S\left(\sqrt{2} b x\right)}{24 \sqrt{2}}-\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}-\frac{\pi  b^3}{16 x}",0,"-(b^3*Pi)/(16*x) - (7*b^3*Pi*Cos[b^2*Pi*x^2])/(48*x) - (b^2*Pi*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(8*x^2) - (7*b^4*Pi^2*FresnelS[Sqrt[2]*b*x])/(24*Sqrt[2]) - (FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(4*x^4) - (b*Sin[b^2*Pi*x^2])/(24*x^3) - (b^4*Pi^2*Defer[Int][(FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/x, x])/8","A",0,0,0,0,-1,"{}"
214,1,163,0,0.2184565,"\int \frac{\text{FresnelC}(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^6} \, dx","Int[(FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/x^6,x]","\frac{\pi ^2 b^4 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{15 x}-\frac{\text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 x^5}-\frac{\pi  b^2 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{15 x^3}-\frac{1}{30} \pi ^3 b^5 \text{FresnelC}(b x)^2-\frac{7}{120} \pi ^2 b^5 \text{Si}\left(b^2 \pi  x^2\right)-\frac{\pi  b^3}{60 x^2}-\frac{b \sin \left(\pi  b^2 x^2\right)}{40 x^4}-\frac{\pi  b^3 \cos \left(\pi  b^2 x^2\right)}{24 x^2}","\frac{\pi ^2 b^4 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{15 x}-\frac{\text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{5 x^5}-\frac{\pi  b^2 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{15 x^3}-\frac{1}{30} \pi ^3 b^5 \text{FresnelC}(b x)^2-\frac{7}{120} \pi ^2 b^5 \text{Si}\left(b^2 \pi  x^2\right)-\frac{\pi  b^3}{60 x^2}-\frac{b \sin \left(\pi  b^2 x^2\right)}{40 x^4}-\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) - (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",13,9,20,0.4500,1,"{6465, 6457, 6441, 30, 3375, 3380, 3297, 3299, 3379}"
215,0,0,0,0.1999669,"\int \frac{\text{FresnelC}(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^7} \, dx","Int[(FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/x^7,x]","\int \frac{\text{FresnelC}(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{\text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)+\frac{\pi ^2 b^4 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{48 x^2}-\frac{\text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{6 x^6}-\frac{\pi  b^2 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{24 x^4}-\frac{1}{45} \sqrt{2} \pi ^3 b^6 \text{FresnelC}\left(\sqrt{2} b x\right)-\frac{7 \pi ^3 b^6 \text{FresnelC}\left(\sqrt{2} b x\right)}{144 \sqrt{2}}-\frac{\pi  b^3}{144 x^3}+\frac{67 \pi ^2 b^5 \sin \left(\pi  b^2 x^2\right)}{1440 x}-\frac{b \sin \left(\pi  b^2 x^2\right)}{60 x^5}-\frac{13 \pi  b^3 \cos \left(\pi  b^2 x^2\right)}{720 x^3}",0,"-(b^3*Pi)/(144*x^3) - (13*b^3*Pi*Cos[b^2*Pi*x^2])/(720*x^3) - (b^2*Pi*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(24*x^4) - (7*b^6*Pi^3*FresnelC[Sqrt[2]*b*x])/(144*Sqrt[2]) - (Sqrt[2]*b^6*Pi^3*FresnelC[Sqrt[2]*b*x])/45 - (FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(6*x^6) + (b^4*Pi^2*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(48*x^2) - (b*Sin[b^2*Pi*x^2])/(60*x^5) + (67*b^5*Pi^2*Sin[b^2*Pi*x^2])/(1440*x) - (b^6*Pi^3*Defer[Int][(Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/x, x])/48","A",0,0,0,0,-1,"{}"
216,0,0,0,0.3141214,"\int \frac{\text{FresnelC}(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^8} \, dx","Int[(FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/x^8,x]","\int \frac{\text{FresnelC}(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{\text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{x^2},x\right)-\frac{1}{84} \pi ^3 b^7 \text{CosIntegral}\left(\pi  b^2 x^2\right)+\frac{\pi ^2 b^4 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{105 x^3}-\frac{\text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{7 x^7}-\frac{\pi  b^2 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{35 x^5}-\frac{\pi  b^3}{280 x^4}+\frac{\pi ^2 b^5 \sin \left(\pi  b^2 x^2\right)}{84 x^2}-\frac{b \sin \left(\pi  b^2 x^2\right)}{84 x^6}-\frac{\pi  b^3 \cos \left(\pi  b^2 x^2\right)}{105 x^4}",0,"-(b^3*Pi)/(280*x^4) - (b^3*Pi*Cos[b^2*Pi*x^2])/(105*x^4) - (b^7*Pi^3*CosIntegral[b^2*Pi*x^2])/84 - (b^2*Pi*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(35*x^5) - (FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(7*x^7) + (b^4*Pi^2*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(105*x^3) - (b*Sin[b^2*Pi*x^2])/(84*x^6) + (b^5*Pi^2*Sin[b^2*Pi*x^2])/(84*x^2) - (b^6*Pi^3*Defer[Int][(Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/x^2, x])/105","A",0,0,0,0,-1,"{}"
217,0,0,0,0.3062786,"\int \frac{\text{FresnelC}(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^9} \, dx","Int[(FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/x^9,x]","\int \frac{\text{FresnelC}(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{\text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{x},x\right)+\frac{\pi ^2 b^4 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{192 x^4}-\frac{\text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{8 x^8}+\frac{\pi ^3 b^6 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{384 x^2}-\frac{\pi  b^2 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{48 x^6}+\frac{853 \pi ^4 b^8 S\left(\sqrt{2} b x\right)}{40320 \sqrt{2}}-\frac{\pi  b^3}{480 x^5}+\frac{187 \pi ^2 b^5 \sin \left(\pi  b^2 x^2\right)}{40320 x^3}-\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{19 \pi  b^3 \cos \left(\pi  b^2 x^2\right)}{3360 x^5}+\frac{\pi ^3 b^7}{768 x}",0,"-(b^3*Pi)/(480*x^5) + (b^7*Pi^3)/(768*x) - (19*b^3*Pi*Cos[b^2*Pi*x^2])/(3360*x^5) + (853*b^7*Pi^3*Cos[b^2*Pi*x^2])/(80640*x) - (b^2*Pi*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(48*x^6) + (b^6*Pi^3*Cos[(b^2*Pi*x^2)/2]*FresnelC[b*x])/(384*x^2) + (853*b^8*Pi^4*FresnelS[Sqrt[2]*b*x])/(40320*Sqrt[2]) - (FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(8*x^8) + (b^4*Pi^2*FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/(192*x^4) - (b*Sin[b^2*Pi*x^2])/(112*x^7) + (187*b^5*Pi^2*Sin[b^2*Pi*x^2])/(40320*x^3) + (b^8*Pi^4*Defer[Int][(FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/x, x])/384","A",0,0,0,0,-1,"{}"
218,1,278,0,0.5203379,"\int \frac{\text{FresnelC}(b x) \sin \left(\frac{1}{2} b^2 \pi  x^2\right)}{x^{10}} \, dx","Int[(FresnelC[b*x]*Sin[(b^2*Pi*x^2)/2])/x^10,x]","-\frac{\pi ^4 b^8 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{945 x}+\frac{\pi ^2 b^4 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{315 x^5}-\frac{\text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{9 x^9}+\frac{\pi ^3 b^6 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{945 x^3}-\frac{\pi  b^2 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{63 x^7}+\frac{\pi ^5 b^9 \text{FresnelC}(b x)^2}{1890}+\frac{83 \pi ^4 b^9 \text{Si}\left(b^2 \pi  x^2\right)}{30240}+\frac{\pi ^3 b^7}{3780 x^2}-\frac{\pi  b^3}{756 x^6}+\frac{67 \pi ^2 b^5 \sin \left(\pi  b^2 x^2\right)}{30240 x^4}-\frac{b \sin \left(\pi  b^2 x^2\right)}{144 x^8}+\frac{5 \pi ^3 b^7 \cos \left(\pi  b^2 x^2\right)}{2016 x^2}-\frac{11 \pi  b^3 \cos \left(\pi  b^2 x^2\right)}{3024 x^6}","-\frac{\pi ^4 b^8 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{945 x}+\frac{\pi ^2 b^4 \text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{315 x^5}-\frac{\text{FresnelC}(b x) \sin \left(\frac{1}{2} \pi  b^2 x^2\right)}{9 x^9}+\frac{\pi ^3 b^6 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{945 x^3}-\frac{\pi  b^2 \text{FresnelC}(b x) \cos \left(\frac{1}{2} \pi  b^2 x^2\right)}{63 x^7}+\frac{\pi ^5 b^9 \text{FresnelC}(b x)^2}{1890}+\frac{83 \pi ^4 b^9 \text{Si}\left(b^2 \pi  x^2\right)}{30240}+\frac{\pi ^3 b^7}{3780 x^2}-\frac{\pi  b^3}{756 x^6}+\frac{67 \pi ^2 b^5 \sin \left(\pi  b^2 x^2\right)}{30240 x^4}-\frac{b \sin \left(\pi  b^2 x^2\right)}{144 x^8}+\frac{5 \pi ^3 b^7 \cos \left(\pi  b^2 x^2\right)}{2016 x^2}-\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) - (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",26,9,20,0.4500,1,"{6465, 6457, 6441, 30, 3375, 3380, 3297, 3299, 3379}"