# Homework Help: Exponential integration

1. Feb 1, 2010

### ronaldoshaky

1. The problem statement, all variables and given/known data

how would you integrate, int (-ik - 2ax)*exp(-2ax^2) dx with limits infinity - infinity

2. Relevant equations

i think i can use the result int exp(-x^2) dx = sqrt (pi). But I am stumped.

3. The attempt at a solution

i thought about multiplying it out

int -ik*exp(-2ax^2) - 2ax*exp(-2ax^2) dx with limits infinity and - infinity

but it looks more complex now. would you use integration by substitution

Thank you
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Feb 1, 2010

### tiny-tim

Welcome to PF!

Hi ronaldoshaky! Welcome to PF!

(have an integral: ∫ and an infinity: ∞ and a pi: π and try using the X2 tag just above the Reply box )

Just do the two parts separately …

-∞ ik e-2ax2 dx you know how to do;

and ∫ 2ax e-2ax2 dx you can do by substitution.

3. Feb 2, 2010

Thank you!

4. Feb 3, 2010

### ronaldoshaky

Hi tiny-tim

Can I evaluate this integral ∫-∞∞ (ik-2ax) exp(-2ax2) dx without multiplying it out,
using integration by parts because it is a product?

I get

∫-∞∞ (ik-2ax) exp(-2ax2) dx = f(x)g(x) - ∫ f '(x)g(x) = - ik (sqrt (pi/2a)) + ikx (sqrt (pi/2a))

Is that any way correct?

5. Feb 3, 2010

No.