To determine The improper integral without using tables. Explanation Given information: 1 ( 1 + v 2 ) ( 1 + tan − 1 v ) Formula: d d x [ tan − 1 x ] = 1 1 + x 2 ∫ c d 1 x d x = [ ln | x | ] c d Calculation: Express the integral as below. ∫ 0 ∞ 1 ( 1 + v 2 ) ( 1 + tan − 1 v ) d v (1) Assume the term u as tan − 1 v . u = tan − 1 v Differentiate with respect to v . d u = 1 1 + v 2 d v When the value of v is 0, the value of u is 0. When the value of v is ∞ , the value of u is π 2 . Substitute u for tan − 1 v and 1 1 + v 2 d v for d u and change the limits of integral in equation (1)

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Chapter 8.8, Problem 19E

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The improper integral without using tables.

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Chapter 8.8, Problem 18E

Chapter 8.8, Problem 20E

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