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The image you've uploaded contains steps for solving an integral. Based on the structure of the work shown in the image, the integration seems to be evaluated using integration by parts. The problem given is:

\[
\int (x^2 + 5x^2 - 2) e^{x} dx
\]

The chosen \( u \) is \( x^2 + 5x^2 - 2 \), and \( dv = e^x dx \). Upon further substitution and steps, the integration is simplified.

The correct answer, based on the detailed steps outlined in the image, appears to be:

\[
u = x^2 + 5x^2 - 2
\]

Let me know if you need further clarification or would like a detailed breakdown of the solution.

### Follow-up questions:

1. Would you like a detailed explanation of the integration by parts process shown?
2. Should I verify the calculations step by step?
3. Do you want to explore alternative methods for solving this integral?
4. Are you looking for additional examples of similar integrals?
5. Do you need clarification on specific steps shown in the image?

**Tip**: When using integration by parts, always double-check your choice of \( u \) and \( dv \) to simplify the problem as much as possible.

Solve the integral ∫(x^2 + 5x^2 - 2) e^x dx using the integration by parts method. This calculus problem involves exponential functions and applying the integration by parts formula. Detailed steps are provided for university-level students.

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