# Limit of Definite Integral #1

Calculus Level 5

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

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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