   Chapter 13.5, Problem 12E ### 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 1-32. Identify the formula used. ∫ x   d s ( 3 x + 2 ) 2

To determine

To calculate: The value of integral xdx(3x+2)2.

Explanation

Given Information:

The provided integral is xdx(3x+2)2.

Formula used:

For any variable u, the integral formula is,

udu(au+b)2=1a2(ln|au+b|+bau+b)+C.

Where, a, b are not a function of u. and C is the constant of integration.

Calculation:

Consider the provided integral:

xdx(3x+2)2

The integral is similar to the integral formula,

udu(au+b)2

Therefore, the formula used is udu(au+b)2=1a2(ln|au+b|+bau+b)+C.

Use the formula udu(au+b)2=1a2(ln|au+b|+bau+b)+C and compare with the provided integral xdx(3x+2)2

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