1. Let's clarify step 3 where we use substitution in integration. 2. We set $u = x^2$ to simplify the integral because the function inside the sine is $x^2$. 3. To change variables, we find the differential $du$, which represents the derivative of $u$ with respect to $x$ times $dx$. 4. Since $u = x^2$, then $\frac{du}{dx} = 2x$, so multiplying both sides by $dx$ gives $du = 2x \, dx$. 5. This means $du$ is the infinitesimal change in $u$ corresponding to an infinitesimal change in $x$. 6. We rearrange to express $x \, dx$ in terms of $du$: $x \, dx = \frac{du}{2}$. 7. This substitution allows us to rewrite the integral in terms of $u$ and $du$, which is easier to integrate. 8. So, $du$ is just a notation for the differential of $u$, used to change variables in integration.