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## anonymous 5 years ago f(x)=x^2*e^(-|x|) how can i solve the integral?

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1. amistre64

i now there are some representations of e^x that cant be integrated.... forget why..

2. amistre64

but for this; just int by parts using x^2 as u; and v as e^...

3. anonymous

Yes, but how i deal the absolute value?

4. amistre64

an absolute value is always positive; and the opposite of an always positive value is always negative right?

5. amistre64

just redefine it; |x| = a perhaps

6. anonymous

Shouldn't i divide the integral into two cases? |x| = x if x>0 and |x| = -x if x<0?

7. amistre64
8. shadowfiend

Yeah, I think that's the way you have to go.

9. watchmath

Is this a definite integral or indefinite?

10. anonymous

The exercise is to solve the integral from -inf to inf

11. watchmath

That makes a difference $$\int_{-\infty}^\infty x^2e^{-|x|}=2\int_0^\infty x^2e^{-x}\,dx$$ and you can use integration by parts.

12. amistre64

thats what I had in mind :) just couldnt spell it out well enough ...

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