The integral you provided is:

\[
\int \cos(3x) \, dx
\]

To solve this integral, we'll use the standard integration formula for \(\cos(ax)\):

\[
\int \cos(ax) \, dx = \frac{1}{a} \sin(ax) + C
\]

Here, \( a = 3 \), so:

\[
\int \cos(3x) \, dx = \frac{1}{3} \sin(3x) + C
\]

where \( C \) is the constant of integration.

Would you like more details or have any questions?

Here are 5 related questions:

1. How would you integrate \(\int \sin(5x) \, dx\)?
2. What is the integral of \(\cos(x^2)\)?
3. How do you differentiate \(\sin(3x)\)?
4. How can substitution be used to solve integrals of the form \(\int \cos(ax+b) \, dx\)?
5. What is the indefinite integral of \(\sec(x)\)?

**Tip:** Always remember to add the constant of integration \( C \) when solving indefinite integrals.

Learn how to solve the integral of cos(3x) with detailed step-by-step instructions. This problem involves using the integration formula for cos(ax) and is suitable for advanced high school students or anyone studying calculus.

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