# Proving the divergent integral of 1/f(x) as x-> infinity

1. Jan 18, 2013

### 000

1. The problem statement, all variables and given/known data
There exists a function f(x) such that the indefinite integral of 1/f(x) as x-> infinity diverges, and f(x) >= x for all values of x. Prove this function must be a linear polynomial.

2. Relevant equations
None that I know of.

3. The attempt at a solution
No idea where to start.

Last edited: Jan 18, 2013
2. Jan 18, 2013

### HallsofIvy

You can't, as stated, it is not true. There exist many non-polynomial functions that are "asymptotic" to x such that the integral of 1/f(x) diverges. However, if you require that f(x) be a polynomial, then it is true that f must be linear.

3. Jan 18, 2013

### 000

f(x) must always be larger than x, are there any asymptotic functions that fit that criteria?

4. Jan 18, 2013