How to Solve this definite integral: $\sqrt{\frac{2}{\pi}} \int\limits^\infty_t \frac{1}{x^2+1} e^{-\frac{x^2}{2}}dx$

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I have a problem to evaluate this definite integral.

Evaluate the definite integral:

$$\sqrt{\frac{2}{\pi}} \int^{\infty}_{t} \frac{1}{x^2+1} e^{-\frac{x^2}{2}}dx$$