   Chapter 5.5, Problem 45E ### 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. ∫ 1 + x 1 + x 2   d x

To determine

To evaluate: The indefinite integral.

Explanation

Given:

The indefinite integral function is 1+x1+x2dx.

Calculation:

Consider u=1+x2

Differentiate both sides of the equation.

du=2xdx12du=xdx

The indefinite integral function is,

1+x1+x2dx=11+x2dx+x1+x2dx (1)

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

11+x2dx+x1+x2dx=11+x2dx+1u(12du)=11+x2dx+121udu (2)

Integrate Equation (2)

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