To integrate \(\sin(3x)\), we can use the basic integration formula for sine functions. The integral of \(\sin(kx)\) is given by:

\[
\int \sin(kx) \, dx = -\frac{1}{k} \cos(kx) + C
\]

In this case, \(k = 3\). So, the integral becomes:

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

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

So, the solution is:

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

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

Here are 5 more questions you can ask:
1. How do you integrate \(\cos(2x)\)?
2. What is the integral of \(\sin^2(x)\)?
3. Can you explain the process of integrating \(\tan(x)\)?
4. How do you integrate \(e^{3x}\)?
5. What is the integral of \(\cosh(x)\)?

**Tip:** When integrating trigonometric functions, look for standard integral formulas that can simplify the process. These formulas are often derived from the basic definitions and properties of the trigonometric functions.

Learn how to integrate sin(3x) with a step-by-step solution. Understand the basic integration formula for sine functions and apply it to solve this specific integral problem. Suitable for advanced high school and college students.

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