I found this result while studying indefinite integral calculus last year.
, where denotes the th derivate of and .
This is basically the generalization of the integral .
It can be seen that . Using integration by parts,
So, is true. Assume, is true i.e .
From our assumption, it follows that,
So, is true. Hence, is true is true. So, by induction, is true .
Also, integrals of the form can be reduced to the aforementioned integral by the substitution .