Integrating Exponential Functions with Sinusoidal Factors

[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?

 

[EmilK]

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?

 

[marlon]

Or complex integration ?


marlon

 

[daniel_i_l]

parts + substitution