Explanation Given: The improper integral is ∫ − ∞ ∞ e x ( 1 + e x ) 2 d x . Formula used: Improper integrals: If f is continuous over an interval and the limit exists, then ∫ a ∞ f ( x ) d x = lim b → ∞ ∫ a ∞ f ( x ) d x . Calculation: Use the substitution method to solve the ∫ − ∞ ∞ e x ( 1 + e x ) 2 d x . Let u = 1 + e x (1) Differentiate on both sides of u = 1 + e x with respect to x . d d x ( u ) = d d x ( 1 + e x ) d u d x = e x d u = e x d x The limits are obtained by substituting in equation (1) as follows. If x = − ∞ , then u = 1 + e − ∞ . That is, u = 1 . If x = ∞ , then u = 1 + e ∞ . That is, u = ∞ . Substitute u = 1 + e x , d u = e x d x and the lower limit 1 and the upper limit ∞ in ∫ − ∞ ∞ e x ( 1 + e x ) 2 d x

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Chapter 11, Problem 31RE

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To find: The value of ∫−∞∞ex(1+ex)2 dx, if it converges.

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Chapter 11, Problem 30RE

Chapter 11, Problem 32RE

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Chapter 11 Solutions

EP CALCULUS FOR BUSINESS..-MYLAB ACCESS

Ch. 11.1 - Evaluate the following, if it converges: 3dx(x1)2.Ch. 11.1 - Prob. 2MP Ch. 11.1 - Prob. 3MP Ch. 11.1 - Prob. 4MP Ch. 11.1 - Prob. 5MP Ch. 11.1 - Prob. 6MP Ch. 11.1 - Prob. 1ED Ch. 11.1 - Prob. 2ED Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E

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The value of ∫ − ∞ ∞ e x ( 1 + e x ) 2 d x , if it converges.

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To find: The value of ∫−∞∞ex(1+ex)2 dx, if it converges.

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Chapter 11 Solutions