   Chapter 13.5, Problem 16E ### 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. ∫ 9 x 2 + 4   d x

To determine

To calculate: The value of integral 9x2+4dx.

Explanation

Given Information:

The provided integral is 9x2+4dx.

Formula used:

The integral formula,

u2+a2du=12(uu2+a2+a2ln|u+u2+a2|)+C.

Calculation:

Consider the provided integral,

9x2+4dx

This expression is similar to that of the formula,

u2+a2du

Therefore, the formula used for this integral is

u2+a2du=12(uu2+a2+a2ln|u+u2+a2|)+C.

Now, use the formula u2+a2du=12(uu2+a2+a2ln|u+u2+a2|)+C and

Compare from the provided expression,

9x2+22(dx)=u2+a2du

In the provided expression, u=3x and a=2.

Let 3x=t

Differentiate with respect to x

3dx=dt

Now, multiply and divide the integral by 3 and write the integrals in terms of t and dt

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