   Chapter 12.2, Problem 31E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Evaluate the integrals in Problems 7-36. Check your results by differentiation. ∫ x 3 − 1 ( x 4 − 4 x ) 3 d x

To determine

To calculate: The value of the integral x31(x44x)3dx.

Explanation

Given Information:

The provided integral is x31(x44x)3dx

Formula used:

The power formula of integrals:

undu=un+1n+1+C (forn1)

The power rule of differentiation:

ddu(un)=nun1

Calculation:

Consider the provided integral:

x31(x44x)3dx

Rewrite the integral by multiplying and dividing by 4 as:

144x34(x44x)3dx

Let u=x44x, then derivative will be,

du=d(x44x)=(4x34)dx

Substitute du for (4x34)dx and u for x44x in provided integration

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