Make me an integral

Calculus Level 3

\[\lim_{n\to\infty}\left(\frac{1}{a+n}+\frac{1}{2a+n}+\frac{1}{3a+n}+\ldots+\frac{1}{na+n}\right)\]

Find the "closed form result" of the limit above.

Here, \(a\gt 0\) is an arbitrary constant such that the expression inside the limit is defined.

\[a\] \[e^a\] \[\dfrac{\ln(\sqrt{a}+1)}{a}\] \[\pi^a\] \[\dfrac{\ln(a+1)}{a}\] \[\pi^e\cdot \ln(a)\] \[\dfrac{\log_{10}(a+1)}{a}\] \[\dfrac{\ln(a+2)}{a}\]

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