   Chapter 4.9, Problem 3E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Find the most general antiderivative of the function. (Check your answer by differentiation.) f ( x ) = 2 x 3 − 2 3 x 2 + 5 x

To determine

To find: The most general antiderivative of the function f(x)=2x323x2+5x and also check the determined antiderivative for the function f(x)=2x323x2+5x by differentiation.

Explanation

Given Data:

Write the given function as follows.

f(x)=2x323x2+5x

Formula used:

The antiderivative function for the function xn is xn+1n+1+C .

Here, C is the constant.

Formula used:

Write the required differentiation formula to verify the answer as follows.

ddx(xn)=nxn1ddx(constant)=0

Calculation:

Rewrite the function f(x)=2x323x2+5x as follows.

f(x)=2x323x2+5x1 (1)

From the antiderivative function formula, the antiderivative function for the function in equation (1) is written as follows.

F(x)=2(x3+13+1)23(x2+12+1)+5(x1+11+1)+C=2(x44)23(x33)+5(x22)+C=12x429x3+52x2+C

Thus, the most general antiderivative of the function f(x)=2x323x2+5x is 12x429x3+52x2+C_

### 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 problems 45-62, perform the indicated operations and simplify. 58.

Mathematical Applications for the Management, Life, and Social Sciences

#### Differentiate. y=x2tanx

Single Variable Calculus: Early Transcendentals

#### Write the following numbers in word form. 2.48

Contemporary Mathematics for Business & Consumers

#### Sometimes, Always, or Never: The sum of two elementary functions is an elementary function.

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

#### True or False: is a convergent series.

Study Guide for Stewart's Multivariable Calculus, 8th 