Explanation Given Information: The provided expression is, ∫ x 2 e − 2 x d x . Formula used: The formula for integration by parts is, ∫ u d v = u v − ∫ v d u Here, u and v be the differentiable functions x . Integral Rule of exponential function: ∫ e n u d u = e n u n + C Here, n is the any number. Calculation: Consider the provided expression: ∫ x 2 e − 2 x d x Let u = x 2 and d v = e − 2 x d x . So, d u = 2 x d x And, v = ∫ d v = ∫ e − 2 x d x = e − 2 x − 2 = − e − 2 x 2 Apply integration by parts to solve integral of ∫ x 2 e − 2 x d x . ∫ x 2 e − 2 x d x = ( x 2 ) ( − e − 2 x 2 ) − ∫ ( − e − 2 x 2 ) ( 2 x d x ) = − x 2 e − 2 x 2 + ∫ x e − 2 x d x Let u = x and d v = e − 2 x d x . So, d u = d x And, v = ∫ d v = ∫ e − 2 x d x = e − 2 x − 2 = − e − 2 x 2 Apply integration by parts to solve integral of ∫ x e − 2 x d x

Calculus: An Applied Approach (MindTap Course List)

10th Edition

ISBN: 9781305860919

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 6.2, Problem 6QY

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To calculate: The solution of indefinite integral ∫x2e−2xdx by the use of integration by parts.

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Chapter 6.2, Problem 5QY

Chapter 6.2, Problem 7QY

Chapter 6 Solutions

Calculus: An Applied Approach (MindTap Course List)

Ch. 6.1 - Prob. 1CP Ch. 6.1 - Prob. 2CP Ch. 6.1 - Prob. 3CP Ch. 6.1 - Prob. 4CP Ch. 6.1 - Prob. 5CP Ch. 6.1 - Prob. 6CP Ch. 6.1 - Prob. 7CP Ch. 6.1 - Prob. 1SWU Ch. 6.1 - Prob. 2SWU Ch. 6.1 - Prob. 3SWU

Ch. 6.1 - Prob. 4SWU Ch. 6.1 - Prob. 5SWU Ch. 6.1 - Prob. 6SWU Ch. 6.1 - Prob. 7SWU Ch. 6.1 - Prob. 8SWU Ch. 6.1 - Prob. 9SWU Ch. 6.1 - Prob. 10SWU Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Integration by Parts In Exercises 5-16, use...Ch. 6.1 - Prob. 6E Ch. 6.1 - Integration by Parts In Exercises 5-16, use...Ch. 6.1 - Prob. 8E Ch. 6.1 - Integration by Parts In Exercises 5-16, use...Ch. 6.1 - Prob. 10E Ch. 6.1 - Integration by Parts In Exercises 5-16, use...Ch. 6.1 - Prob. 12E Ch. 6.1 - Integration by Parts In Exercises 5-16, use...Ch. 6.1 - Prob. 14E Ch. 6.1 - Integration by Parts In Exercises 5-16, use...Ch. 6.1 - Prob. 16E Ch. 6.1 - Prob. 17E Ch. 6.1 - Prob. 18E Ch. 6.1 - Prob. 19E Ch. 6.1 - Prob. 20E Ch. 6.1 - Finding an Indefinite Integral In Exercises 17-38,...Ch. 6.1 - Finding an Indefinite Integral In Exercises 17-38,...Ch. 6.1 - Prob. 23E Ch. 6.1 - Prob. 24E Ch. 6.1 - Finding an Indefinite Integral In Exercises 17-38,...Ch. 6.1 - Prob. 26E Ch. 6.1 - Prob. 27E Ch. 6.1 - Prob. 28E Ch. 6.1 - Prob. 29E Ch. 6.1 - Prob. 30E Ch. 6.1 - Prob. 31E Ch. 6.1 - Prob. 32E Ch. 6.1 - Prob. 33E Ch. 6.1 - Prob. 34E Ch. 6.1 - Prob. 35E Ch. 6.1 - Prob. 36E Ch. 6.1 - Finding an Indefinite Integral In Exercises 17-38,...Ch. 6.1 - Finding an Indefinite Integral In Exercises 17-38,...Ch. 6.1 - Prob. 39E Ch. 6.1 - Prob. 40E Ch. 6.1 - Prob. 41E Ch. 6.1 - Evaluating a Definite Integral In Exercises 39-46,...Ch. 6.1 - Prob. 43E Ch. 6.1 - Prob. 44E Ch. 6.1 - Prob. 45E Ch. 6.1 - Prob. 46E Ch. 6.1 - Prob. 47E Ch. 6.1 - Prob. 48E Ch. 6.1 - Prob. 49E Ch. 6.1 - Prob. 50E Ch. 6.1 - Prob. 51E Ch. 6.1 - Prob. 52E Ch. 6.1 - Verifying Formulas In Exercises 53 and 54, use...Ch. 6.1 - Verifying Formulas In Exercises 53 and 54, use...Ch. 6.1 - Prob. 55E Ch. 6.1 - Prob. 56E Ch. 6.1 - Prob. 57E Ch. 6.1 - Prob. 58E Ch. 6.1 - Prob. 59E Ch. 6.1 - Prob. 60E Ch. 6.1 - Prob. 61E Ch. 6.1 - Prob. 62E Ch. 6.1 - Prob. 63E Ch. 6.1 - Prob. 64E Ch. 6.1 - Prob. 65E Ch. 6.1 - Revenue A company sells a seasonal product. 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The solution of indefinite integral ∫ x 2 e − 2 x d x by the use of integration by parts.

Solution Summary: The author calculates the solution of indefinite integral displaystyle 'int' by using integration by parts.

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To calculate: The solution of indefinite integral ∫x2e−2xdx by the use of integration by parts.

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Chapter 6 Solutions