Can you give any advice on how to find or approximate the following integral $$ F(t,y) = \int_{0}^{y}\frac{i e^{-\frac{3 t^2 \left(x^2+1\right)}{2 \left(9 x^2+1\right)}-i \frac{4 t^2 x}{9 x^2+1}}}{\sqrt{(x-i) (3 x+i)}} dx, $$ where $t,y \in \mathbb{R}$, $i$ - imaginary unit. More generally, I need to find or approximate the following integral $$ G(y) = \int_{-\infty}^{\infty}|F(t,y)|^2 dt $$ (If we talk about the method of steepest descent, I don't see a big parameter $\lambda$ here)
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