Answer
Diverges
Work Step by Step
\begin{aligned}
\int_{0}^{\infty} \frac{d x}{(x+1)} &=\lim _{R \rightarrow \infty} \int_{0}^{R} \frac{d x}{(x+1)} \\ &=\lim _{R \rightarrow \infty}\ln (x+1)\bigg|_{0} ^{R} \\ &=\lim _{R \rightarrow \infty}\ln (R+1)\\
&=\infty \end{aligned}
Thus, the integral diverges.
