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

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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
 
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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! =)
 
OH YEAH! DONT IGNORE THE ABSOLUTE VALUE...cause e^(-x) is a lot different that e^(x)...do you have limits on that integral?
 
Just factor out a: |ax| = |a||x|. Keep the absolute sign there. Integration by parts works fine. Just do it twice.
 
Thank you!
 
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