   Chapter 12.2, Problem 17E ### 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 7-36. Check your results by differentiation. ∫ ( x − 1 ) ( x 2 − 2 x + 5 ) 4 d x

To determine

To calculate: The value of the integral (x1)(x22x+5)4dx and also check the solution by differentiation.

Explanation

Given Information:

The provided integral is (x1)(x22x+5)4dx.

Formula used:

The power formula of integrals, if u=u(x), then,

undu=un+1n+1+C

According to the power rule of derivative,

ddx(xn)=nxn1

Calculation:

Consider the provided integral,

(x1)(x22x+5)4dx

Rewrite the integral by multiplying and dividing by 2 as,

122(x1)(x22x+5)4dx

Consider the power rule of integrals,

undu=un+1n+1+C

Now, to use the power rule, the integrand should have the function u(x) and its derivative u(x) and n1.

Let, u=x22x+5 and n=4

Differentiate u=x22x+5 with respect to x and get,

du=(2x2)dx

Now, all required parts are present, so the integral is of the form,

122(x1)(x22x+5)4dx=

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### In Exercises 516, evaluate the given quantity. log1,000

Finite Mathematics and Applied Calculus (MindTap Course List)

#### Multiply: (7)(3)

Elementary Technical Mathematics

#### The interval of convergence of is: [−1, 1] [−1, 1) (−1, 1] (−1, 1)

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

#### For , f′(x) =

Study Guide for Stewart's Multivariable Calculus, 8th 