Solve this with lower incomplete gamma function

[Alexitron]

Homework Statement

\int e^{-\frac{2Zr}{a}}*r^{-1}dr Boundaries:[0,R]

Homework Equations

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The Attempt at a Solution

I tried to solve this with lower incomplete gamma function and got \gamma(0,\frac{2ZR}{a}) which is infinite i think.
Z=81,a:Bohr radius,R=r0*A^(1/3) ,Th:A=203,r0=1,2*10^(-13)

 

[CompuChip]

I don't know what the lower incomplete gamma function is, but Mathematica gives me
\int_\epsilon^R \frac{1}{r} e^{-2Zr/a} \, \mathrm dr = \gamma(0, 2Z\epsilon/a) - \gamma(0, 2ZR/a)
which is finite for \epsilon > 0 but diverges for \epsilon \to 0.