Find the integral by using the simplest method. Not all problems require integration by parts. [x²e*dx Oe* (-x² – 2x – 2) + C | Oe-* (x² + 2x + 2) + C Oe* (x² – 2x + 2) + C Oe-* (x² – 2x – 2) + C
Find the integral by using the simplest method. Not all problems require integration by parts. [x²e*dx Oe* (-x² – 2x – 2) + C | Oe-* (x² + 2x + 2) + C Oe* (x² – 2x + 2) + C Oe-* (x² – 2x – 2) + C
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![## Problem Statement
Find the integral by using the simplest method. Not all problems require integration by parts.
\[ \int x^2 e^{-x} \, dx \]
### Choices:
1. \( \circ \, e^{-x} \left( -x^2 - 2x - 2 \right) + C \)
2. \( \circ \, e^{-x} \left( x^2 + 2x + 2 \right) + C \)
3. \( \circ \, e^{-x} \left( x^2 - 2x + 2 \right) + C \)
4. \( \circ \, e^{-x} \left( x^2 - 2x - 2 \right) + C \)
### Explanation
This problem involves finding the integral of the function \( x^2 e^{-x} \). The result contains several expressions in the answer choices, each with a constant \( C \) to account for the integration constant. Evaluate the integral step-by-step to determine the correct option.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F30c07f2b-13db-4887-9bcb-8633a00a882e%2F52bf23f7-be80-49b3-aa19-9c864e711952%2Fv5otdiw_processed.png&w=3840&q=75)
Transcribed Image Text:## Problem Statement
Find the integral by using the simplest method. Not all problems require integration by parts.
\[ \int x^2 e^{-x} \, dx \]
### Choices:
1. \( \circ \, e^{-x} \left( -x^2 - 2x - 2 \right) + C \)
2. \( \circ \, e^{-x} \left( x^2 + 2x + 2 \right) + C \)
3. \( \circ \, e^{-x} \left( x^2 - 2x + 2 \right) + C \)
4. \( \circ \, e^{-x} \left( x^2 - 2x - 2 \right) + C \)
### Explanation
This problem involves finding the integral of the function \( x^2 e^{-x} \). The result contains several expressions in the answer choices, each with a constant \( C \) to account for the integration constant. Evaluate the integral step-by-step to determine the correct option.
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