   Chapter 12, Problem 5T ### 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 1-11. 5.   ∫ 6 x 2 ( 7 + 2 x 3 ) 9   d x

To determine

To calculate: The integral 6x2(7+2x3)9dx.

Explanation

Given Information:

The integral is;

6x2(7+2x3)9dx

Formula used:

The power rule of integration is;

The integration of function f(x)=xn is given by;

xndx=xn+1n+1+c n1

Here c is any arbitrary constant.

The sum rule is;

f(x)±g(x)dx=f(x)dx±g(x)dx

Calculation:

Provided integral is;

6x2(7+2x3)9dx

Rearrange the above integral as,

6x2(7+2x3)9dx=6x2(7+2x3)9dx

Apply integral substitution

Consider that u=2x3, then, du=6x2dx, thus, the function becomes;

6x2(7+2x3)9dx=(7+u)9du

Again, apply integral substitution as;

v=(7+u)d

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