   Chapter 13.5, Problem 15E ### 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. ∫ x 5 x 2 d x

To determine

To calculate: The value of integral x5x2dx.

Explanation

Given Information:

The provided integral is x5x2dx.

Formula used:

For any variable u, the integral formula is,

audu=aulogae+C          =aulna+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:

x5x2dx

Multiply and divide the integral by 2,

125x2(2xdx)

Let x2=t,

Now, differentiate both the sides,

2xdx=dt

So the expression can now be written as,

125tdt

The integral is similar to the integral formula,

audu

Therefore, the formula used is

audu=au

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