$$\int\limits\limits_{0}^{∞} x^2e^{-2y|x|}dx = \left[ 2/(2y)^{3} \right] (\lim 0,∞)$$ \

can someone explaine this

Question

$$\int\limits\limits_{0}^{∞} x^2e^{-2y|x|}dx = \left[ 2/(2y)^{3} \right] (\lim 0,∞)$$ \

can someone explaine this

unklerhaukus · Answer

please disregard the (lim 0 ,∞) bit

jamesj · Answer

First, you can drop the absolute value signs as x is non-negative in the domain of integration.

Then integrate by parts twice.  E.g., first time u' = exp(-xy), v = x^2

then you'll need to integrate and third time and get the result.

jamesj · Answer

make that u' = exp(-2xy)

unklerhaukus · Answer

integration by parts, three times, ...bother.

well at least i know it will work.
 thanks

jamesj · Answer

the third time isn't by parts -- you'll see.