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