What is the integal of e^(x^2)x^4 from negative infinity to infinity?
The function is an even function ie
Now, let's integrate.
At first sight, you have to use the integration by parts, this must be almost a reflex when you see an exponential. The exponential will very often take the place of the v' function in :
So you must make appear the derivate of , 2x, so as to be able to integrate :
the integrate of will simply be
------ integration by parts ------
the derivate of is
(the two limits tend to 0)
In the same way, make appear the derivate of so as to integrate once again by parts.
And there, i can't help anymore because of the last integral : i don't remember how to do