Math Challenge

[Marty]

Can anyone figure out this integral:

integral of (x^2)exp(x)exp(-x^2)dx

Good luck...

 

[agnitrate]

Originally posted by: Marty
Can anyone figure out this integral:

integral of (x^2)exp(x)exp(-x^2)dx

Good luck...

Maybe if you wrote it in a coherent fashion....

-silver

 

[bleeb]

looks like an integration by parts, substitution (U) and exponential identities. Good Luck

 

[Marty]

What is incoherent about that?

integral of x^2 * exp(x) * exp(-x^2) * dx

btw, exp(x) = e^x

 

[agnitrate]

Originally posted by: Marty
What is incoherent about that?

integral of x^2 * exp(x) * exp(-x^2) * dx

btw, exp(x) = e^x

Sorry, I just have never seen e^x represented as exp(x).

-silver

 

[Orsorum]

So it's x^2 * e^{-x^3}?

 

[agnitrate]

Originally posted by: Zakath15
So it's x^2 * e^{-x^3}?

I think that's what it should be.

Here's a hint : Think power rule.

-silver

 

[AgentEL]

Originally posted by: agnitrate

Originally posted by: Zakath15
So it's x^2 * e^{-x^3}?

I think that's what it should be.

Here's a hint : Think power rule.

-silver

isn't it x^2 * e^{x-x^2}

 

[Heisenberg]

I did it on wolfram's integrator site b/c I don't have my TI-89 handy. The answer's pretty complicated:
E^(x-x^2) *(1/4 - x/2) + (3/8)*E^1/4 * sqrt(pi) * Erf [1/2 (-1 + 2x)]

 

[RaynorWolfcastle]

Originally posted by: Zakath15
So it's x^2 * e^{-x^3}?

I highly doubt it's what he originally posted since e^(-x^2) doesn't have a closed form AFAIK... it's got to be e^(-x^3) given the context of the problem

 

[bleeb]

Originally posted by: Heisenberg
I did it on wolfram's integrator site b/c I don't have my TI-89 handy. The answer's pretty complicated:
E^(x-x^2) *(1/4 - x/2) + (3/8)*E^1/4 * sqrt(pi) * Erf [1/2 (-1 + 2x)]

CHEATER =)

 

[agnitrate]

Originally posted by: AgentEL

Originally posted by: agnitrate

Originally posted by: Zakath15
So it's x^2 * e^{-x^3}?

I think that's what it should be.

Here's a hint : Think power rule.

-silver

isn't it x^2 * e^{x-x^2}

Ah yeah, my fault. That's what I get for not thinking

-silver

 

[Marty]

So it's x^2 * e^{-x^3}?

No, its x^2 * e^(x - x^2)

 

[eLiu]

uh...it's not e^(-x^3), it's e^(x-x^2), although the former is MUCH more doable than the latter. Maple yields this for the latter:

-1/2*x*exp(x-x^2)-1/4*exp(x-x^2)+3/8*Pi^(1/2)*exp(1/4)*erf(x-1/2)

erf is some sort of an error function, but I forgot exactly how it works.

 

[RaynorWolfcastle]

Originally posted by: eLiu
uh...it's not e^(-x^3), it's e^(x-x^2), although the former is MUCH more doable than the latter. Maple yields this for the latter:

-1/2*x*exp(x-x^2)-1/4*exp(x-x^2)+3/8*Pi^(1/2)*exp(1/4)*erf(x-1/2)

erf is some sort of an error function, but I forgot exactly how it works.

*sigh* it refers to the solution not being of closed form. Does anyone actually read what I write?