To find the integral of \(34x^5 \, dx\), we use the power rule for integration. The power rule states:

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

where \(n \neq -1\) and \(C\) is the constant of integration.

For the given integral:

\[
\int 34x^5 \, dx
\]

We can factor out the constant 34:

\[
34 \int x^5 \, dx
\]

Now apply the power rule where \(n = 5\):

\[
34 \cdot \frac{x^{5+1}}{5+1} + C = 34 \cdot \frac{x^6}{6} + C
\]

Simplify the expression:

\[
\frac{34}{6} x^6 + C = \frac{17}{3} x^6 + C
\]

Therefore, the integral of \(34x^5 \, dx\) is:

\[
\frac{17}{3} x^6 + C
\]

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

Would you like more details, or do you have any questions?

Here are 5 related questions for further exploration:

1. What is the integral of \( x^4 \, dx \)?
2. How do you integrate a polynomial function like \(3x^2 + 2x + 1\)?
3. What are the rules for integrating a function with multiple terms?
4. How does the power rule change when integrating a function like \(x^{-3} \, dx\)?
5. What happens when integrating functions with fractional exponents?

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

Learn how to find the integral of 34x^5 dx using the power rule for integration with a detailed step-by-step solution. This problem covers integration concepts, including the power rule and constant of integration. Suitable for students in Grades 11-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation