Given, differential equation is,
$$
\begin{aligned}
& d x\left(1+y+x^2 y\right)+\left(x+x^3\right) d y=0 \\
\Rightarrow \quad & \frac{d y}{d x}=-\left[\frac{1+y+x^2 y}{x+x^3}\right]
\end{aligned}
$$
$$
\begin{aligned}
& \Rightarrow \quad \frac{d y}{d x}=-\left\{\frac{1}{x\left(1+x^2\right)}+\frac{\left(1+x^2\right) y}{x\left(1+x^2\right)}\right\} \\
& \Rightarrow \quad \frac{d y}{d x}-\frac{y}{x}=-\frac{1}{x\left(1+x^2\right)} \\
&
\end{aligned}
$$
Here, $p=-\frac{1}{2}, Q=-\frac{1}{x\left(1+x^2\right)}$
$$
\begin{aligned}
\text { Integrating factor } & \equiv e^{\int p d x} \\
& =e^{\int\left(-\frac{1}{x}\right)} d x \\
& =e^{-\log x} \\
& =e^{\log \left(\frac{1}{x}\right)} \\
& =\frac{1}{x}
\end{aligned}
$$