To solve the integral \( \int -3x^5 \, dx \), we can use the power rule for integration, which states:

\[
\int x^n \, dx = \frac{x^{n+1}}{n+1} + C, \quad \text{where} \, n \neq -1
\]

Now apply the rule to the given function:

1. Factor out the constant \(-3\):
\[
\int -3x^5 \, dx = -3 \int x^5 \, dx
\]

2. Apply the power rule:
\[
-3 \cdot \left( \frac{x^{5+1}}{5+1} \right) + C = -3 \cdot \left( \frac{x^6}{6} \right) + C
\]

3. Simplify:
\[
\frac{-3x^6}{6} + C = \frac{-x^6}{2} + C
\]

So, the solution is:
\[
\int -3x^5 \, dx = \frac{-x^6}{2} + C
\]

Would you like further explanation or have any questions?

Here are 5 related questions:
1. What is the general formula for the power rule of integration?
2. How would you integrate \( \int 5x^4 \, dx \)?
3. How do you handle the integration of negative powers, such as \( \int x^{-2} \, dx \)?
4. What is the constant of integration and why is it important?
5. How would you verify the result of this integral by differentiation?

**Tip:** Always remember to add the constant \( C \) when performing indefinite integrals!

Learn how to compute the integral ∫(-3x^5) dx using the power rule of integration. This step-by-step solution simplifies the integral and applies key calculus concepts, making it suitable for students in Grades 11-12.

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