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# integration by parts giving a singular point watch

1. Hi I'm trying to integrate this function by parts:

where f and e^ are 0 at infinity.
I would expect to get

however this function has a singular point at eta=0, how do I deal with this?
2. (Original post by yehyeh123)
Hi I'm trying to integrate this function by parts:

where f and e^ are 0 at infinity.
I would expect to get

however this function has a singular point at eta=0, how do I deal with this?
If you're doing a pure course, you don't: you can find functions f with f->0 and divergent (both when eta = 0 and when it isn't).

If you're doing an applied course, you generally assume everything will come out OK, in which case you either specifically handle the case by rewriting , or you can calculate the integral for eta non-zero and just assume it remains valid when eta = 0 as well.

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Updated: February 1, 2010
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