integral of Gaussian function and rational function

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Can any one with Mathematica help me with following integrals? O know those have closed -forms

\begin{equation} \int_{-\infty}^{\infty} \frac{x^4}{(a+bx^2)^2} e^{\frac{-x^2}{2c}} dx \end{equation}

\begin{equation} \int_{-\infty}^{\infty} \frac{x^3}{(a+bx^2)^2} e^{\frac{-x^2}{2c}} dx \end{equation}

a,b,c are real and positive.