   Chapter 13.5, Problem 8E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Evaluate the integrals in Problems 1-32. Identify the formula used. 8.   ∫ 1 5 d q q 25 + q 2

To determine

To calculate: The value of the integral 15dqq25+q2.

Explanation

Given Information:

The provided integral is 15dqq25+q2

Formula used:

For any variable u, the integral formula is,

duua2+u2=1aln|a+a2+u2u|+C

Where, ‘a’ is not a function of u. and C is the constant of integration.

Calculation:

Consider the provided integral,

15dqq25+q2

The integral can be rewritten as:

15dqq52+q2

The denominator of the integral is similar to that of the denominator in the integral formula,

duua2+u2

Therefore, the formula used is duua2+u2=1aln|a+a2+u2u|+C

Now, use the formula duua2+u2=1aln|a+a2+u2u|+C and compare from the provided integral 15dqq25+q2

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