# Tail for the integral of a diffusion process

I would like to compute the following tail, $$\mathbb{P}\left(\int_{0}^{T} f(X_t)\mathrm{dt}>x\right),$$ assuming $$\mathbb{P}[f(X_t)>x] = x^{-\alpha} \log(x),$$ and $X$ is a diffusion process, meaning that $\mathrm{dX_t}= b(X_t) \mathrm{dW_t}+ c(X_t)\mathrm{dt}$ where $W$ is a Brownian motion, and $b$ and $c$ are given functions. Thanks in advance.

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