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

[000]

Homework Statement

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.

Homework Equations

None that I know of.

The Attempt at a Solution

No idea where to start.

 

[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.

 

[000]

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.

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

 

[Dick]

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

How about f(x)=x+1/x?