Question

\( \int (x + 1)(x - x^2) e^x \, dx \) is equal to

• A. \( (x + 1)e^x + C \)
• B. \( (x - 1)e^x + C \)
• C. \( e^x + C \)
• D. \( (x + 1)e^x + C \)

Hint:

To solve integrals involving exponential functions, consider using integration by parts or simplifying the expression.

Answer 1

The Correct Option is C

Step 1: Simplifying the expression.
The integral is solved by breaking down the expression and using integration by parts. After solving, we find that the result is \( e^x + C \).

Step 2: Conclusion.
The integral evaluates to \( e^x + C \), corresponding to option (3).