The value of the definite integral
\[
\int_{0}^{1}\frac{xe^{x}}{(x+1)^2}\,dx
\]
is equal to
Show Hint
Whenever the integrand contains
\[
\frac{xe^x}{(x+1)^2},
\]
check whether it is
\[
\boxed{
\frac{d}{dx}
\left(
\frac{e^x}{x+1}
\right)
}
\]
This makes the integration immediate.