https://r2.erweima.ai/mathbot/image/1726955338989cz3p6c04.jpg

The image contains an integral expression:

\[
\int \frac{x^4 \, dx}{ab} = \frac{x^5}{5ab} + C
\]

### Solution:

1. The given expression is a basic indefinite integral problem. The integral is:

\[
\int \frac{x^4}{ab} \, dx
\]

Here, \(a\) and \(b\) are constants, so they can be factored out of the integral:

\[
\frac{1}{ab} \int x^4 \, dx
\]

2. The integral of \(x^4\) is:

\[
\int x^4 \, dx = \frac{x^5}{5}
\]

3. Applying this, we get:

\[
\frac{1}{ab} \cdot \frac{x^5}{5} = \frac{x^5}{5ab}
\]

4. Therefore, the final answer is:

\[
\frac{x^5}{5ab} + C
\]

This matches the right-hand side of the equation given in the image.

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Would you like further details on this, or do you have any questions?

Here are some related questions for practice:

1. What is the integral of \(\frac{x^3}{a^2b}\)?
2. How would you compute \(\int x^2 \, dx\)?
3. Can you solve \(\int \frac{x^6}{ab} \, dx\)?
4. How do you approach integrating polynomial functions in general?
5. What is the role of constants in integrals and how do they affect the solution?

**Tip:** Always factor out constants before integrating—it simplifies the process!

Learn how to solve the indefinite integral of x^4 divided by ab. This problem covers key calculus concepts, including basic integration of polynomial functions. Suitable for high school seniors and university freshmen.

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