   Chapter 8.3, Problem 43E

Chapter
Section
Textbook Problem

Using a Product-to-Sum Formula In Exercises 43-48, find the indefinite integral. ∫ cos 2 x cos 6 x   d x

To determine

To calculate: The value of the indefinite integral cos2xcos6xdx.

Explanation

Given:

The indefinite integral:

cos2xcos6xdx

Formula used:

Trigonometric identity:

2cosCcosD=cos(CD)+cos(C+D)

The integral formulas:

cos(ax)dx=1asin(ax)+C

Calculation:

Multiply the numerator and denominator of the integral by 2 and solve further as follows:

cos2xcos6xdx=12(2cos2xcos6x)dx=12(cos(2x6x)+cos(2x+6x))dx=12(cos<

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