   Chapter 5.5, Problem 47E ### 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 ( 2 x + 5 ) 8 d x

To determine

To evaluate: The indefinite integral.

Explanation

Given:

The indefinite integral function is x(2x+5)8dx.

Calculation:

Consider u=2x+5 (1)

Differentiate both sides of the equation.

du=2dxdx=12du

Rearrange the terms of the Equation (1).

2x=u5x=12(u5)

The indefinite integral function is,

x(2x+5)8dx (2)

Substitute x for 12(u5), u for (2x+5), and (12du) for dx in Equation (2).

x(2x+5)8dx=12(u5)u8(12du)=14(u5)u8du=14(u95u8)du=14(u9du5u8du) (3)

Integrate Equation (3)

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