To solve the integral $\int dx$, we use the fact that differentiation and integration are inverse operations. Here, we need to find a function $F(x)$ such that $F'(x) = 1$.

The differentiation rule we use is the power rule for derivatives. For a function $x^n$, the derivative is given by:

$\frac{d}{dx} x^n = n x^{n-1}$

In this case, we consider $n = 1$:

$\frac{d}{dx} x = 1$

Thus, the function $x$ has a derivative of 1. Therefore, the integral of 1 with respect to $x$ is $x$, plus a constant of integration $C$. This gives us:

$\int dx = x + C$

Would you like any more details or have any questions about this solution?

Here are 8 related questions for further exploration:

1. How do you apply the power rule for integration?
2. What is the integral of $x^3$ with respect to $x$?
3. Can you explain the product rule for differentiation?
4. How do you find the integral of $a$ with respect to $x$, where $a$ is a constant?
5. What is the chain rule for differentiation?
6. How do you solve the integral $\int (2x+3) dx$?
7. What is the integral of $\frac{1}{x}$ with respect to $x$?
8. How do you differentiate $e^{x^2}$?

Tip: To verify your integration results, you can differentiate the antiderivative. If you get the original function back, your integration is correct.