   Chapter 13.6, Problem 27E ### 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 25-30, select the formula or method (I-IV) that should be used to evaluate each integral. Then evaluate the integral.Integration by partsII. ∫ e u   d u III. ∫ d u u IV. ∫ d u u ∫ e x e x + 1   d x

To determine

To calculate: The value of the integral exex+1dx.

Explanation

Given Information:

The provided integral is exex+1dx.

Formula used:

According to the power rule of integrals,

undu=un+1n+1+C

Differential formula

d(ex)dx=ex

Calculation:

Consider the provided integral:

exex+1dx

The integral is similar to the formula undu.

Now to evaluate further,

Now, let ex+1=u, and differentiate by the use of differential formula d(ex)dx=ex

exdx=du

Thus, the integral becomes,

exex+1dx=u1/2du

Now, use the power formula of integrals,

un<

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