Let's solve the integrals shown in the image:

a. $\int 5 \, dx$

The integral of a constant multiplied by $dx$ is straightforward. We integrate the constant $5$ with respect to $x$, which is:

$\int 5 \, dx = 5x + C$ where $C$ is the constant of integration.

b. $\int du$

The integral of $du$ (which implies a constant function) is simply:

$\int du = u + C$ again, $C$ is the constant of integration.

Would you like further details or have any questions on these integrals?

Here are five related questions to expand your understanding:

1. What is the integral of $\int 7 \, dx$?
2. How would you integrate $\int (3x + 2) \, dx$?
3. What is the significance of the constant $C$ in indefinite integrals?
4. How does the power rule for integration apply when integrating polynomials?
5. What happens when you differentiate the result of an indefinite integral?

Tip: The constant of integration $C$ appears in indefinite integrals because the process of differentiation removes constant terms, so we reintroduce one during integration to account for this.