Solving Integral Problem: x*exp(iax + b)

[Void123]

Homework Statement

integral[x*exp(iax + b)] dx

Homework Equations

The Attempt at a Solution

I know there is a an integral for this I can pull out from a table, but is there any direct analytical way to solve it? Perhaps by parts?

Thanks.

 

[jbunniii]

Homework Statement

integral[x*exp(iax + b)] dx

Homework Equations

The Attempt at a Solution

I know there is a an integral for this I can pull out from a table, but is there any direct analytical way to solve it? Perhaps by parts?

Thanks.

You can use

$$e^{iax + b} = e^{iax} e^b$$

to simplify the integrand. Yes, integration by parts looks promising.

 

[Void123]

What if I had $$\int^{\infty}_{-\infty}x exp(-ax^{2})exp(bx) dx$$

 

[lanedance]

haven't tried it... but how about combining the exponetial terms, then complete the square in the exponential, substitute for y = x+c in the square, then use another substitution u = y^2

the only problem i can see is in you integration limits... may have to have a think about those & maybe split the integral