https://file.aiquickdraw.com/mathbot/file/1725860779250xhdkt0es.jpg

It seems that the image text extraction wasn't successful. I'll analyze the image visually to help interpret the math problem.

From the provided image, the equation seems to be:

\[
\int \frac{x^3}{x^2 + 4} \cdot \text{tan}^{-1}\left(\frac{x}{2}\right) dx
\]

Would you like a detailed solution for this integral? If yes, I can proceed with solving it.

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Here are 5 related questions:
1. What is the general method for solving integrals involving inverse trigonometric functions?
2. How do you approach integrals with products of algebraic and trigonometric functions?
3. What are the common techniques used for integration by parts?
4. How does substitution work in simplifying integrals?
5. Can integrals involving tangent inverse functions always be solved analytically?

**Tip**: When dealing with complex integrals, breaking the expression into simpler parts can make the solution easier.

Learn how to solve the integral ∫ (x^3 / (x^2 + 4)) * tan^(-1)(x/2) dx with a detailed step-by-step solution. This problem involves advanced calculus concepts, including integration by parts and inverse trigonometric functions, suitable for undergraduate students.

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