Hi,(adsbygoogle = window.adsbygoogle || []).push({});

This integral seems to be coming up a fair bit in questions involving normalisation of wave functions

[tex]\int x^2\exp{(-ax^2)}dx[/tex]

and my tutor and lecturer both say to just use the fact that

[tex]x^2\exp{(-ax^2)}=-\frac{d}{da}\exp{(-ax^2)}[/tex]

my question simply is how do we use this. it may be obvious can you say

[tex]\int x^2\exp{(-ax^2)}dx=\int-\frac{d}{da}\exp{(-ax^2)}dx=\int-\frac{dx}{da}\exp{(-ax^2)}d=-\frac{dx}{da}\exp{(-ax^2)}[/tex]

...?

cheers for any help,

Bart

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# Integration Trickiness

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