Chapter 8.3, Problem 8E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Finding an Indefinite Integral Involving Sine and Cosine In Exercises 3-14, find the indefinite integral. ∫ cos 3 x 3   d x

To determine

To calculate: The Indefinite integral of the expression.

Explanation

Given:

The expression is âˆ«cos3x3dx.

Calculation:

Consider the integral to be I,

I=âˆ«cos3x3dx

Simplify it to a form, such that power rule can be used,

I=âˆ«cos3x3dx=âˆ«(cos2x3)cosx3dx=âˆ«(1âˆ’sin2x3)cosx3dx=âˆ«cosx3dxâˆ’âˆ«sin2x3cosx3dx

For the integral involve power of sine and cosine,

Letâ€‰â€‰â€‰â€‰u=sinx3du=cosx33d

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