   Chapter 13.5, Problem 18E ### 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. 18.   ∫ x x 4 − 36   d x

To determine

To calculate: The value of integral xx436dx.

Explanation

Given Information:

The provided integral is xx436dx.

Formula used:

For any variable u, the integral formula is,

u2a2du=12(uu2a2a2ln|u+u2a2|)+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

Calculation:

Consider the provided integral:

xx436dx

Multiply and divide the integral by 2,

12(x2)2(6)2(2xdx)

Let x2=t,

Differentiate both the sides,

2xdx=dt

So the integral becomes,

12t2(6)2dt

The integral is similar to the integral formula,

u2a2du

Therefore, the formula used is u2a2du=12(uu2a2a2ln|u+u2a2|)+C

Now, use the formula u2

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