   Chapter 6.1, Problem 2CP ### 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
1 views

# Checkpoint 2Find ∫ 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.

eaxdx=eaxa+C

Calculation:

Consider the indefinite integral xlnxdx

Here,

dv=xdx and u=lnx

First find v,

dv=xdxdv=xdx

On further solving,

v=x22 …… (1)

Now 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=x22lnxx221xdx=x22lnx&#

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