To find the integral of the expression \( 65x^4 \), follow the power rule for integration:

\[
\int x^n \, dx = \frac{x^{n+1}}{n+1} + C
\]

For \( 65x^4 \):

\[
\int 65x^4 \, dx = 65 \cdot \frac{x^{4+1}}{4+1} + C = 65 \cdot \frac{x^5}{5} + C = \frac{65}{5} x^5 + C = 13x^5 + C
\]

Thus, the integral is:

\[
13x^5 + C
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. What is the integral of \( x^3 \)?
2. How do you apply the power rule for negative exponents?
3. What is the definite integral of \( 65x^4 \) from \( x = 1 \) to \( x = 2 \)?
4. How would you differentiate \( 13x^5 + C \)?
5. How does the constant of integration, \( C \), affect the graph of the integral?

**Tip:** Always add the constant \( C \) when computing indefinite integrals!

This guide explains how to compute the integral of 65x^4 by applying the power rule of integration. Learn how the integral is simplified step-by-step to 13x^5 + C, with a clear explanation of the power rule formula and its application. Ideal for high school students in Grades 11-12 studying calculus.

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