   Chapter 6.1, Problem 32E ### 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.) ∫ ln 2 x x 2   d x

To determine

To calculate: The value of indefinite integral ln2xx2dx.

Explanation

Given Information:

The provided indefinite integral is ln2xx2dx.

Formula used:

The integration by parts udv=uvvdu.

Where, u and v are function of x.

xndx=xn+1n+1,n1

Calculation:

Consider the indefinite integral ln2xx2dx

Here,

dv=1x2dx and u=ln2x

First find v,

dv=1x2dxdv=1x2dx

On further solving,

v=1x …...…... (1)

Now find du,

u=ln2x

Differentiate both side with respect x,

dudx=d(ln2x)dxdudx=1x

And,

du=1xdx …...…... (2)

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

ln2xx2dx=ln2xx1x1xdx=ln2xx+1<

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