3. The monotonic increasing interval of the function $f(x)=(x+1) \ln (x+1)$ is $\qquad$
$$
f^{\prime}(x)=\ln (x+1)+(x+1) \cdot \frac{1}{x+1}=\ln (x+1)+1>0 \Rightarrow x>\frac{1}{\mathrm{e}}-1,
$$

Therefore, the monotonic increasing interval of the function $f(x)=(x+1) \ln (x+1)$ is $\left(\frac{1}{\mathrm{e}}-1,+\infty\right)$.