$\displaystyle \lim_{n\rightarrow \infty}n\int_{-1}^{0}(x+e^x)^ndx$

The answer it's suppose to be

$\displaystyle

\frac{1}{2}

$

So the value of the integral should be

$\displaystyle

\frac{1}{2n}

$

Direct integration is nonsense.

With First mean value theorem for integration I don't obtain anything.