Explanation Given: The expression is ∫ 8 x − 4 e 2 x d x . Formula used: Write the integration by part formula: ∫ u d v = u v − ∫ v d u Calculation: Consider the following expression: ∫ 8 x − 4 e 2 x d x Simplify: ∫ 8 x − 4 e 2 x d x = ∫ 8 x − 4 ( e − 2 x ) d x Assume u = 8 x − 4 . Determine d u by take a derivative: d u = 8 d x Assume d v = e − 2 x d x . Determine v by taking an anti-derivative. ∫ d v = ∫ e − 2 x d x v = − 1 2 e − 2 x Recall the integration by part formula: ∫ u d v = u v − ∫ v

Mathematics with Applications, Books a la Carte, and MyLab Math with Pearson eText - Title-Specific Access Card Package (12th Edition)

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Author: Lial

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Chapter 13.3, Problem 8E

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To calculate: The value of the expression ∫8x−4e2xdx by using the integration by parts.

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Chapter 13.3, Problem 7E

Chapter 13.3, Problem 9E

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Mathematics with Applications, Books a la Carte, and MyLab Math with Pearson eText - Title-Specific Access Card Package (12th Edition)

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The value of the expression ∫ 8 x − 4 e 2 x d x by using the integration by parts.

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