Explanation Given: The provided expression is: ∫ x 5 e x 2 d x Formula used: Integration by part: ∫ u d v = u v − ∫ d u ⋅ v Calculation: The given integration is I = ∫ x 5 e x 2 d x . Substitute, t = x 5 x = t 1 5 d x = 1 5 d t From the integration, I = 1 5 ∫ t 1 5 e t 2 5 d t …… (1) Again substitute, p = t 2 5 t = p 5 2 d t = 5 2 d p Therefore, I = 1 2 × 5 2 ∫ e p p 2 d p …… (2) Integrate on right hand side by using integration by parts. Let, u = p 2 d u = 2 p d p And d v = e p v = e p Now, substitute these values in the formula for integration by parts

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Chapter 8.2, Problem 65E

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To calculate: The indefinite integaral ∫x5ex2dx by using substituation followed by integration by part.

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Chapter 8.2, Problem 64E

Chapter 8.2, Problem 66E

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Chapter 8 Solutions

CALCULUS EARLY TRANSCENDENTAL FUNCTIONS

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The indefinite integaral ∫ x 5 e x 2 d x by using substituation followed by integration by part.

Solution Summary: The author calculates the indefinite integaral using substituation followed by integration by part.

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To calculate: The indefinite integaral ∫x5ex2dx by using substituation followed by integration by part.

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Chapter 8 Solutions