What should be the strategy to solve these type of integrals. And how to solve this integral.
$\lim_{n \rightarrow \infty}{\int_ 0^1}\frac{n x^{n-1}}{1+x}dx$
I tried to solve it by substitution: multiplying and deviding by $x^n$ and substibution $t=x^n$ I got this
$\lim_{n \rightarrow \infty}{\int_ 0^1}\frac{1}{1+x^{1/n}}dx$
and don't know what to do now.