Integral of x^(1/2)*e^(-x) from -∞ to ∞

[snoweangel27]

I can't seem to figure this integral out
$$\int$$x^(1/2)*e^(-x) dx
from -$$\infty$$ to $$\infty$$

I have tried integrating by parts, but that didn't seem to do any good. Does anyone know a good way to start this problem?

 

[dextercioby]

Y not make $$x=t^2$$ ?

 

[sennyk]

Are we restricted to the reals? If so, then the limits of integration are not in the domain.

 

[D H]

Substituting x=t² does not yield a Gaussian. As sennyk noted, the integration limits cannot be -infinity to infinity.

 

[Midy1420]

break the integral into two parts one from -inf to 0 and then 0 to inf...if any of those two intregrals diverge then the whole thing diverges

 

[d_leet]

break the integral into two parts one from -inf to 0 and then 0 to inf...if any of those two intregrals diverge then the whole thing diverges

The problem is more that the function isn't even defined on one of those intervals.