   Chapter 8.3, Problem 85E

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 sec4(2πx5)dx.

Explanation

Given:

The provided expression is sec4(2πx5)dx.

Formula used:

The integration rule for secnxdx=1n1secn2xtanx+n2n1secn2xdx.

Calculation:

Consider the integral, sec4(2πx5)dx.

Recall the integration rule is secnxdx=1n1secn2xtanx+n2n1secn2xdx.

Here n is 4 and x is 2πx5.

Multiply the equation by 52π to make it equivalent to x.

sec4(2πx5)dx=52π[13sec2(2πx5)tan(2πx5)+23sec2(2πx5)dx]

Further, use the integration rule as secnxdx=1n1secn2xtanx+n2n1secn2xdx again

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