Find integrals

1. Dec 9, 2006

firenze

Find the two integrals:
$$\int_0^{\infty}\frac{e^{-\alpha x^2}}{x^2+1}\sin(\alpha x) \, dx$$
$$\int_0^{\infty}e^{-\beta^2t}\cos(\beta x) \, d\beta$$

Any hint?

2. Dec 9, 2006

EmilK

As you have not provided any of your own work, that is all I can give. You should have some kind of book or lists with definition of some ways to perform integration, such as reverse chain rule, u substitution, integration by parts and so on.

Which one(s) can you apply here?

3. Dec 9, 2006

marlon

Or complex integration ???

marlon

4. Dec 10, 2006

daniel_i_l

parts + substitution