   Chapter 12, Problem 21RE ### 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 1-26. 22. ∫ 6 x 7 ( 5 x 8 + 7 ) 3 d x

To determine

To calculate: The value of the integral 6x7(5x8+7)3dx.

Explanation

Given Information:

The provided integral is 6x7(5x8+7)3dx.

Formula used:

According to the power rule of integrals,

xndx=xn+1n+1+C

Calculation:

Consider the provided integral:

6x7(5x8+7)3dx

Rewrite the provided integral by dividing by multiplying by 40 as,

64040x7(5x8+7)3dx

Now, let 5x8+7=t, then on obtaining differentials,

40x7dx=dt

Thus, the integral becomes,

64040x7(5x8+7)3dx=320dtt3

Now, use power rule of integral as,

64040x7(5x8+7)3dx=320dtt3=3

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