   Chapter 12.2, Problem 32E ### 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. ∫ 3 x 5 − 2 x 3 ( x 6 − x 4 ) 5 d x

To determine

To calculate: The value of the integral 3x52x3(x6x4)5dx.

Explanation

Given Information:

The provided integral is 3x52x3(x6x4)5dx

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:

3x52x3(x6x4)5dx

Rewrite the integral by multiplying and dividing by 2 as:

126x54x3(x6x4)5dx

Let u=x6x4, then derivative will be,

du=d(x6x4)=(6x54x3)dx

Substitute du for (6x54x3)dx and u for x6x4 in provided integration

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