Some remarks on integral parameters of Wiener process

We consider integrals $tau_{rho}=int_0^1rhoxi^2,dx$, where $xi$ is Wiener process and $rho$ is generalized function from some class of multipliers. In the case when multiplier $rho$ belongs to the trace-class, it is shown that $tau_{rho}$ has $chi^2$-distribution (or analogous). An example of multiplier $rho$ not belonging to the trace-class is constructed.