   Chapter 5.5, Problem 48E ### 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 indefinite integral. ∫ x 3 x 2 + 1   d x

To determine

To evaluate: The indefinite integral.

Explanation

Given:

The indefinite integral function is x3x2+1dx.

Calculation:

Consider the follows:

u=x2+1x2=u1

Differentiate both sides of the equation.

2xdx=duxdx=12du

The indefinite integral function is,

x3x2+1dx=x2x2+1xdx (1)

Substitute x2 for (u1), u for (x2+1), and (12du) for (xdx) in Equation (1).

x2x2+1xdx=(u1)u(12du)=12(u1)u12du=12(u32u12)du=12(u31duu12du) (2)

Integrate Equation (2)

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