Answer
$y=\sqrt[3] {3 \ln |x+1| +C}$
Work Step by Step
We are given that $\dfrac{dy}{dx}=\dfrac{1}{(x+1)y^2}$
We will separate the variables to obtain:
$y^2 \ dy=\dfrac{dx}{x+1}$
Integrate to obtain:
$\int y^2 \ dy=\int \dfrac{dx}{x+1}$
This implies that $\dfrac{y^3}{3}=\ln |x+1|+C$
Therefore, we have: $y=\sqrt[3] {3 \ln |x+1| +C}$
