# Find integrals

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?

## Answers and Replies

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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?
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?

Or complex integration ???

marlon

daniel_i_l
Gold Member
parts + substitution