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hello, I would like to compute the following tail

$ \mathbb{P}\left( \left[ \int_{0}^{T} f(X_t)dt \right] >x\right) $ if $ \mathbb{P}[f(X_t)>x] = x^{-\alpha} \log(x) $

X is a Diffusion process meaning that $ dX_t = b(X_t) dW_t + c(X_t)dt $ where $W$ is a brownian motion, $b$ et $c$ are given functions\ Thanks in advance

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