How Do You Integrate ∫x²e^(-2|ax|) dx with Absolute Values?

[Felicity]

Homework Statement

∫x²e^-2|ax| dx

The Attempt at a Solution

tried to integrate by parts but I just ended up with a more difficult integral including an x³ times the e^-2|ax|

I've also tried substituting y=2ax

to get 1/(2a)∫y²e^-y dx

but where do i go from there? and can I just ignor the absolute value?


Can anybody recommend another strategy? How can I accommodate the absolute value?

Thank you

 

[Thorn]

Well, yeah...intergrate by parts! and try to reduce x^2! that is write e^(whatever) as the u'...so that when you apply the formula, you actually differentiate x^2...thus making it 2x...then do it again...and make it 2...then you will have nothing more than an integral with e(whatever that was)...You were just applying the formula wrong...and probably writing x^2 as (1/3*x^3)' ...DONT DO THAT! =)

 

[Thorn]

OH YEAH! DONT IGNORE THE ABSOLUTE VALUE...cause e^(-x) is a lot different that e^(x)...do you have limits on that integral?

 

[Defennder]

Just factor out a: $$|ax| = |a||x|$$. Keep the absolute sign there. Integration by parts works fine. Just do it twice.

 

[Felicity]

Thank you!