   Chapter 12, Problem 8RE ### 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. 8 .  ∫ 5 x 2 (3 x 3 +7) 6 d x

To determine

To calculate: The value of the integral 5x2(3x3+7)6dx.

Explanation

Given Information:

The provided integral is 5x2(3x3+7)6dx.

Formula used:

According to the power formula of integrals:

xndx=xn+1n+1+C

Calculation:

Consider the provided integral,

5x2(3x3+7)6dx

Now, rewrite the above integral by multiplying and dividing by 9 as,

5x2(3x3+7)6dx=599x2(3x3+7)6dx

Now, let 3x3+7=t.

Differentiate both sides by x,

9x2dx=dt

Thus, the integral becomes,

5x2(3x3+7)6dx=599x2(3x3+7)6dx=59t6dt

Now, use the power rule of integrals to obtain the above integral as:

5x2(3x3+7)6dx=59

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