   Chapter 4.5, Problem 5E

Chapter
Section
Textbook Problem

# Evaluate the integral by making the given substitution. ∫ x 3 ( x 4 − 5 ) 2 d x ,    u = x 4 − 5

To determine

To evaluate:

The integral x3x4-52 dx by making the given substitution u=x4-5.

Explanation

1) Concept:

i) The substitution rule is that

If u=g(x) is a differentiable function whose range is an interval I and f is continuous oninterval I, then f(gx)g'xdx=f(u)du.

ii) Indefinite integral

xn dx=xn+1n+1+C   (n-1)

2) Given:

x3x4-52 dx     u=x4-5

3) Calculation:

Use the substitution u=x4-5

Differentiate u=(x4-5) with respect to x

du=4x3dx

As x3 dx is a part of the integration, solving for x3 dx by dividing both side by 4

### 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

#### Evaluate the integral. 14(4+6uu)du

Single Variable Calculus: Early Transcendentals, Volume I

#### Convert the expressions in Exercises 6584 to power form. 35x5x8+72x3

Finite Mathematics and Applied Calculus (MindTap Course List)

#### In Exercises 2932, find the value(s) of x that satisfy the expression. 29. 2x2 + 3x 2 0

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

#### Find the value of the sum. 31. i=1n(i2+3i+4)

Single Variable Calculus: Early Transcendentals

#### True or False: is conservative.

Study Guide for Stewart's Multivariable Calculus, 8th 