Explanation Given information: The indefinite integral ∫ sin 2 x tan x d x Formula used: The integral formula ∫ x n d x = x n + 1 n + 1 + C & ∫ tan x d x = − ln | cos x | + C , where C is an arbitrary. The differential formula d d x ( cos x ) = − sin x The trigonometric identity sin 2 x + cos 2 x = 1 Calculation: To evaluate ∫ sin 2 x tan x d x First simplify this using trigonometric identity as ∫ sin 2 x tan x d x = ∫ ( 1 − cos 2 x ) tan x d x = ∫ tan x d x − ∫ cos 2 x tan x d x = ∫ tan x d x − ∫ cos 2 x sin x cos x d x = ∫ tan x

Loose-Leaf Version for Calculus: Early Transcendentals Single Variable

4th Edition

ISBN: 9781319312886

Author: Rogawski, Jon, Adams, Colin, FRANZOSA, Robert

Publisher: W. H. Freeman

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Chapter 7.6, Problem 45E

To determine

Evaluate the integral

∫sin2xtanxdx

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Chapter 7.6, Problem 44E

Chapter 7.6, Problem 46E

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Chapter 7 Solutions

Loose-Leaf Version for Calculus: Early Transcendentals Single Variable

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