Partition function lennard jones potential

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Derivator
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hi folks,

I want to calculate the potential energy part of the partition function of 2 particles interacting via the Lennard-Jones potential. This partition function should be proportional to:

[itex]\int_0^\infty exp(-\beta * 4((\frac{1}{r})^{12}-(\frac{1}{r})^6)) dr[/itex]

But this integral won't converge, since the integrand is approx. equal to 1 for large r.

What is my mistake?
derivator
 
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