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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Integration by Parts In Exercises 5-16, use integration by parts to find the indefinite integral. See Examples 1, 2, 3, and 4.

x e 3 x   d x

To determine

To calculate: The value of indefinite integral xe3xdx.

Explanation

Given Information:

The provided indefinite integral is xe3xdx.

Formula used:

The integration by parts udv=uvvdu.

Where, u and v are function of x.

eaxdx=eaxa+C

Calculation:

Consider the indefinite integral xe3xdx

Here,

dv=e3xdx and u=x

First find v,

dv=e3xdxdv=e3xdx

On further solving,

v=e3x3 …… (1)

Now 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,

xe3xdx=xe3x3e

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