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1 Ju'e" du = u'e n-1 eau au Use the formula not integration by parts, a to evaluate / = fx'e*dx

1 Ju'e" du = u'e n-1 eau au Use the formula not integration by parts, a to evaluate / = fx'e*dx

Calculus: Early Transcendentals
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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**Using a Specific Integration Formula** To evaluate the integral \( I = \int x^2 e^x \, dx \), use the following integration formula instead of integration by parts: \[ \int u^n e^{au} \, du = \frac{1}{a} u^n e^{au} - \frac{n}{a} \int u^{n-1} e^{au} \, du \] This formula provides a method to integrate functions of the form \( u^n e^{au} \), useful for avoiding the more complex process of integration by parts.
Transcribed Image Text:**Using a Specific Integration Formula** To evaluate the integral \( I = \int x^2 e^x \, dx \), use the following integration formula instead of integration by parts: \[ \int u^n e^{au} \, du = \frac{1}{a} u^n e^{au} - \frac{n}{a} \int u^{n-1} e^{au} \, du \] This formula provides a method to integrate functions of the form \( u^n e^{au} \), useful for avoiding the more complex process of integration by parts.
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The given integral is ∫x2exdx

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