\[ \large I_n =\int_0^1 \frac{x^n}{ax+b} \, dx \]

Define the integral \(I_n\) as above for positive real variables \(a\) and \(b\) independent of \(x\) and natural number \(n\).

\[ \large \lim_{n\to\infty} n I_n = \frac1{\lambda a + \mu b } \]

If \(\lambda \) and \(\mu\) are constants that satisfy the limit above, evaluate \( \lambda + \mu \).

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