Is it possible to find the integral of ##f(x)/x^2##?

MevsEinstein
TL;DR Summary
What the title says
I am creating an integration technique and I have only one step left! I need to integrate ##f(x)/x^2## and then I'll be done. So I want to know if integrating this is possible.

Wolfram Alpha can't integrate it, but there are problems that it couldn't solve, so I'm not 100% sure that Wolfram Alpha is right.

Homework Helper
Gold Member
Oops

Gold Member
You'll need to tell us about f(x) and the domain. Some functions just aren't integrable. For example, if ##f(x)=x##, ##\int_{-1}^1 \frac{1}{x} \, dx## doesn't work. Wolfram Alpha told me so.

For arbitrary f(x), the answer is no.

Mark44
Mentor
You can't get an explicit solution without knowing what f(x) is. You can use integration by parts to express the integral in terms of integrals or derivatives of f(x). For some f(x) this can lead to simpler expressions, but that depends on f(x).

Homework Helper
So what if ##f(x)## has a domain that accepts all integers?
That does not narrow things down very much.

If you have a function that is integrable and you undefine it at all integers, it does not become unintegrable.

Homework Helper
Gold Member
So what if ##f(x)## has a domain that accepts all integers?
That doesn't help because:

You'll need to tell us about f(x)
For arbitrary f(x), the answer is no.
You can't get an explicit solution without knowing what f(x) is.

Not sure how many different ways we can say the same thing.