(I have asked the question
[The commutativity of minimal extension $\cdots$][1] and I deduce this question to the next simple question:)

Let $X$ be a rational variety over $\mathbb{C}$, $\phi : \hat{X} \rightarrow X$ be the blow-up, and $M$ be a simple (holonomic) $D_{\hat{X}}$-module.
Then

*Is it true that the direct image $\int_{\phi}M (=\phi_+M)$ is also simple (holonomic) $D_X$-module ?*


  [1]: https://mathoverflow.net/questions/301134/the-commutativity-of-minimal-extension-and-direct-image-by-blowing-down