Let's solve the integrals shown in the image.

a. $\int 5 \, dx$

To integrate a constant, you multiply the constant by the variable of integration, in this case $x$, and then add the constant of integration $C$:

$\int 5 \, dx = 5x + C$

b. $\int du$

The integral of $du$ is simply the variable $u$ plus the constant of integration $C$:

$\int du = u + C$

Solutions:

• a. $\int 5 \, dx = 5x + C$
• b. $\int du = u + C$

Would you like any further details or explanations on these integrals?

Here are some related questions:

1. What happens when you integrate a variable instead of a constant?
2. How does the power rule apply to integration?
3. What is the general formula for integrating constants?
4. How would you handle definite integrals with these expressions?
5. How does differentiation relate to integration?

Tip: When integrating a constant, always remember to add the constant of integration $C$, as indefinite integrals represent a family of functions.