   Chapter 6.1, Problem 20E ### 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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# Finding an Indefinite Integral In Exercises 17-38, find the indefinite integral. (Hint: Integration by parts is not required for all the integrals.) ∫ x e − 2 x   d x

To determine

To calculate: The value of indefinite integral xe2xdx.

Explanation

Given Information:

The provided indefinite integral is xe2xdx.

Formula used:

The integration by parts udv=uvvdu.

Where, u and v are function of x.

eaxdx=eaxa+C

Calculation:

Consider the indefinite integral xe2xdx

Here,

dv=e2xdx and u=x

First find v,

dv=e2xdxdv=e2xdx

On further solving,

v=e2x2 …...…... (1)

Find du:

u=x

Differentiate both side with respect x;

dudx=dxdxdudx=1

And,

du=1dx …...…... (2)

Apply integration by parts formula and substitute equation (1) and (2) in udv=uvvdu,

xe2x=x(e2x2)e2x21dx

Apply the formula eaxdx=eaxa+C,

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