   Chapter 13.7, Problem 16E ### 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

# In Problems 1-20, evaluate the improper integrals that converge. ∫ − ∞ − 2 5 3 x + 5 d x

To determine

To calculate: The value of the improper integral 253x+5dx if it converges.

Explanation

Given Information:

The provided integral is,

253x+5dx

Formula used:

According to the logarithmic rule of integrals,

x1dx=ln|x|+C

If the limit defining the improper integral is a unique finite number, then integral converges else it diverges,

bf(x)dx=limaabf(x)dx

Calculation:

Consider the provided integral,

253x+5dx

Now, use the formula,

bf(x)dx=limaabf(x)dx

To rewrite the integral as,

253x+5dx=limaa253x+5dx

Now, divide and multiply the integral by 3,

lima53a2(3x+5)13dx

Let, 3x+5=u

Differentiate with respect to x

3dx=du

So, the expression becomes,

lima53

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