Explanation 1) Concept: i) The substitution rule If u = g ( x ) is a differentiable function whose range is an interval I and f is continuous on I , then ∫ f ( g x ) g ' x d x = ∫ f ( u ) d u ii) Indefinite integral ∫ sec ⁡ t tan ⁡ t d t = sec ⁡ t + C 2) Given: ∫ sec ⁡ 3 t tan ⁡ 3 t d t 3) Calculation: Here, use the substitution method because by substituting u = 3 t the given integral become a simpler integral. Substitute u = 3 t . Differentiate u = 3 t with respect to t . d u = 3 d t Divide by 3 on both sides

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Author: Stewart

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Chapter 4.5, Problem 13E

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The indefiniteintegral ∫sec⁡3ttan⁡3tdt

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Chapter 4.5, Problem 12E

Chapter 4.5, Problem 14E

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The indefiniteintegral ∫ sec ⁡ 3 t tan ⁡ 3 t d t

Solution Summary: The author evaluates the indefinite integral by substituting u=3t and dividing by 3 on both sides.

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To evaluate:

The indefiniteintegral ∫sec⁡3ttan⁡3tdt

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Chapter 4 Solutions

The indefiniteintegral ∫ sec ⁡ 3 t tan ⁡ 3 t d t

Solution Summary: The author evaluates the indefinite integral by substituting u=3t and dividing by 3 on both sides.

Concept explainers

Videos

To evaluate: The indefiniteintegral ∫sec⁡3ttan⁡3tdt

Want to see the full answer?

Chapter 4 Solutions

To evaluate:

The indefiniteintegral ∫sec⁡3ttan⁡3tdt