To determine The value of the integral. Explanation Given information: ∫ x 2 + 4 x + 3 x + 2 d x Formula: tan 2 x = sec 2 x − 1 d d x sec x = sec x tan x ∫ sec 2 θ d θ = tan θ + C ∫ x n d x = x n + 1 n + 1 + C Calculation: Express the integral as below. ∫ x 2 + 4 x + 3 x + 2 d x = ∫ x 2 + 4 x + 4 − 1 ( x + 2 ) d x ∫ x 2 + 4 x + 3 x + 2 d x = ∫ ( x + 2 ) 2 − 1 ( x + 2 ) d x (1) Apply trigonometric substitution by assuming the variable x + 2 as sec θ . x + 2 = sec θ Differentiate the variable x with respect to θ . d x d θ = sec θ tan θ d x = sec θ tan θ d θ Consider this term ( x + 2 ) 2 − 1 by substituting sec θ for x + 2 . ( x + 2 ) 2 − 1 = ( sec θ ) 2 − 1 = tan 2 θ = tan θ Substitute sec θ for x + 2 , sec θ tan θ d θ for d x and tan θ for ( x + 2 ) 2 − 1 in equation (1)

Thomas' Calculus: Early Transcendentals plus MyLab Math with Pearson eText -- Title-Specific Access Card Package (14th Edition)

14th Edition

ISBN: 9780134768496

Author: Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher: PEARSON

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Chapter 8.4, Problem 51E

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The value of the integral.

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Chapter 8.4, Problem 50E

Chapter 8.4, Problem 52E

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