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I've been trying to work out the normalization of this probability distribution but have found very few resources that have dealt with this. (one being: https://www.tandfonline.com/doi/abs/10.1080/00401706.1978.10489702). Can anyone help me in solving this? Additionally, I also wanted to know the astronomical relevance of this distribution (Where in astrophysics/cosmology does this distribution come up?)
Any help is much appreciated.
$$\int_{\infty}^{+\infty} exp ([ax + bx^2]^2) dx$$
$$a\&b\in R$$
$$a\&b\in R$$