   Chapter 8.3, Problem 86E

Chapter
Section
Textbook Problem

# Using Formulas In Exercises 83–86, use the results of Exercises 79–82 to find the integral. ∫ sec ⁡ 4 ( 2 π x / 5 ) d x

To determine

To calculate: The value of integral sin4xcos2xdx.

Explanation

Given:

The provided expression is sin4xcos2xdx.

Formula used:

The integration rule is cosmxsinnxdx=cosm+1xsinn1xm+n+n1m+ncosmxsinn2xdx.

Calculation:

Consider the integral sin4xcos2xdx.

Recall the integration rule is cosmxsinnxdx=cosm+1xsinn1xm+n+n1m+ncosmxsinn2xdx.

sin4xcos2xdx=cos3xsin3x6+36cos2xsin2xdxsin4xcos2xdx=cos3xsin3x6+12cos2xsin2xdx

Further, use the integration rule is cosmxsinnxdx=cosm+1xsinn1xm+n+n1m+ncosmxsinn2xdx again

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