solve the differential equation by integrating directly I am trying to solve a differential equation and I don't know how to solve it when it comes to integrating directly. I'd like to know how to do this so I can start doing other problems. Thanks in advance.
Solve the differential equation by integrating directly
$${{\rm d}y \over {\rm d} t} = {4t + 4 \over \left(t + 1\right)^{2}}$$

$$y'(t)=4t+\frac4{(t+1)^2}\implies y(t)=2t^2+\frac{4t}{t+1}+y(0)$$
$$y'(t)=\frac{4t+4}{(t+1)^2}\implies y'(t)=\frac{4}{t+1}\implies y(t)=4\log(t+1)+y(0)$$
The solution of the second version on the interval $(-\infty,-1)$ would be
$$
y(t)=4\log|t+1|+y(-2).
$$
