   Chapter 13.5, Problem 26E ### 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. ∫ d x 9 − ( 2 x + 3 ) 2

To determine

To calculate: The value of integral dx9(2x+3)2.

Explanation

Given Information:

The provided integral is dx9(2x+3)2.

Formula used:

For any variable u, the integral formula is,

dua2u2=12aln|a+uau|+C

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

Differentiation of un with respect to u is nun1.

Where n is any real number.

Calculation:

Consider the provided integral:

dx9(2x+3)2

Multiply and divide the integral by 2.

122dx32(2x+3)2

Let, 2x+3=t

Differentiate both the sides,

2dx=dt

So the integral now becomes,

12dt32t2

Now, use the formula dua2u2=12

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