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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 ln x d x

To determine

To calculate: The value of indefinite integral xlnxdx.

Explanation

Given Information:

The provided indefinite integral is xlnxdx.

Formula used:

The integration by parts udv=uvvdu.

Where, u and v are function of x.

xndx=xn+1n+1+C,n1

Calculation:

Consider the indefinite integral xlnxdx

Here,

dv=x12dx and u=lnx

First find v,

dv=x12dxdv=x12dx

On further solving,

v=23x32 …...…... (1)

Find du:

u=lnx

Differentiate both side with respect x;

dudx=d(lnx)dxdudx=1x

And,

du=1xdx …...…... (2)

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

xlnxdx=23x32lnx23x321xdx

Apply the formula xndx=xn+1n+1+C,n1,

xlnxdx=23x32ln

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