It seems like your input is a bit unclear. Are you asking to solve an integral expression involving \( \frac{35}{x^3} \) with respect to \(x\)? If so, the integral can be written as:

\[
\int \frac{35}{x^3} \, dx
\]

Let's go ahead and solve it.

### Solution:

First, rewrite the integrand:

\[
\frac{35}{x^3} = 35x^{-3}
\]

Now, apply the power rule for integration:

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

Here, \(n = -3\), so:

\[
\int 35x^{-3} \, dx = 35 \cdot \frac{x^{-2}}{-2} + C = -\frac{35}{2x^2} + C
\]

Thus, the integral of \( \frac{35}{x^3} \, dx \) is:

\[
-\frac{35}{2x^2} + C
\]

### Final Answer:

\[
\int \frac{35}{x^3} \, dx = -\frac{35}{2x^2} + C
\]

Do you have any questions about this? Would you like to explore details or a specific part?

Here are 5 related questions to expand your understanding:
1. How does the power rule of integration work for different powers of \(x\)?
2. What happens if the power of \(x\) is \( -1 \) in an integral?
3. How do you find definite integrals involving power functions?
4. Can you solve the same integral for different constants other than 35?
5. How do you check if your integration result is correct?

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

Solve the integral of 35 / x^3 using the power rule for integration. This solution provides a step-by-step approach to finding the integral, which is useful for calculus 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