   Chapter 6.1, Problem 54E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Verifying Formulas In Exercises 53 and 54, use integration by parts to verify the formula. ∫ x n e a x   d x = x n e a x a − n a ∫ x n − 1 e a x   d x ,   n > 0

To determine

To prove: The indefinite integral xneaxdx=xneaxanaxn1eaxdx,n>0.

Explanation

Given Information:

The provide indefinite integral is xneaxdx.

Formula used:

xndx=xn+1n+1,n1,d(xn)dx=nxn1,eaxdx=eaxa+C

Proof:

Consider the indefinite integral xneaxdx

Here,

dv=eaxdx and u=xn

First find v,

dv=eaxdxdv=eaxdx

On further solving,

v=eaxa

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