How to perform this integration?

[xmtung]

Homework Statement

The integration:

 

[rock.freak667]

...I can't view the picture...try re-upping it as a jpeg or something so

 

[xmtung]

I re-upload the pic. The integration is that ∫cos(kx)exp[(-αt)K^2] dkfrom zero to infinity

 

[Dick]

Convert cos(kx) to (exp(ikx)+exp(-ikx))/2. Combine the exponentials and complete the squares in the exponents. Now do a change of variable and use the known result for exp(-Cx^2).