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}