Need help to solve integral (cos^2 (ax)*e^(ibx)dx)

[cikicdragan]

I need help to solve this integeral (acctualy I know result but I need process):
integral (cos^2 (ax)*e^(ibx)dx)
Where "i" means imaginary unit.

 

[royhaas]

Re: Need help to solve integral

Rewrite the cosine function \(\displaystyle cos^2(ax)=\frac{1+cos(2ax)}{2}\). Now you have two integrals, the second of which you may use integration by parts, or use a complex exponential representation and then take the real part of the result.