w****o
发帖数: 20 | 1 My Mathematica shows that:
Integrate[Exp[-x^2]*Sin[x^2]/x^2,{x,-Infinity,
Infinity}]=2^(5/4)*Pi^(1/2)*Sin[Pi/8]=1.613;
Integrate[Exp[-x^2]*Sin[x]^2/x^2,{x,-Infinity,
Infinity}]=Sqrt[Pi]*(-1+1/e+Sqrt[Pi]*Erf[1])=1.527;
I think you can do your integral analytically (integration by parts):
Exp[-x^2]*Sin[x]^2/x^2 dx
=-Exp[-x^2]*Sin[x]^2 d(1/x)
=...
Finally you can reduce the integrand into a linear combination of
Integrate[Exp[-x^2]*Sin[x]/x] and Integrate[Exp[-x^2]*Sin[x]], which you all
know how t |
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