   Chapter 5.5, Problem 19E ### 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. ∫ a + b x 2 3 a x + b x 3 d x

To determine

To evaluate: The indefinite integral.

Explanation

Given:

The indefinite integral function is a+bx23ax+bx3dx.

Calculation:

Consider u=3ax+bx3

Differentiate both side of the Equation.

du=(3ax+3bx2)dx=[3(a+bx2)]dxdx=13(a+bx2)du

The indefinite integral function is,

a+bx23ax+bx3dx (1)

Substitute u for (3ax+bx3) and (13(a+bx2)du) for dx in Equation (1).

a+bx23ax+bx3dx=a+bx2u(13(a+b

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