   Chapter 5, Problem 27RE ### 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

# Evaluate the integral, if it exists. ∫ x + 2 x 2 + 4 x d x

To determine

The value of the integral function.

Explanation

Given information:

The integral function is x+2x2+4xdx.

Consider (x2+4x) as u.

u=x2+4x (1)

Differentiate both sides of the Equation.

du=(2x+4)dx=2(x+2)dx (2)

Rearrange Equation (2) to find the value of (x+4)dx as shown below:

(x+2)dx=12du (3)

Substitute u for (x2+4x) and 12du for (x+2)dx in the function as shown below:

x+2x2+4xdx=1u12du=

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Study Guide for Stewart's Multivariable Calculus, 8th 