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## Main Question or Discussion Point

Could anyone please explain how to solve the improper integral below?

I have no idea of how to do it.

If f is a bounded non-negative function, then show that

the integral from zero to infinity of f(x+1/x)*ln(x)/x dx=0.

Thank you.

I have no idea of how to do it.

If f is a bounded non-negative function, then show that

the integral from zero to infinity of f(x+1/x)*ln(x)/x dx=0.

Thank you.