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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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Finding an Indefinite Integral In Exercises 17-38, find the indefinite integral. (Hint: Integration by parts is not required for all the integrals.)

x x 1 d x

To determine

To calculate: The value of indefinite integral xx1dx.

Explanation

Given Information:

The provided indefinite integral is xx1dx.

Formula used:

The integration by parts udv=uvvdu.

Where, u and v are function of x.

(ax+b)ndx=1a(ax+b)n+1n+1,n1

Calculation:

Consider the indefinite integral xx1dx

Here,

dv=(x1)12dx and u=x

First find v,

dv=(x1)12dxdv=(x1)12dx

On further solving,

v=(x1)12(12)=2x1 …...…... (1)

Now find du,

u=x

Differentiate both side with respect x,

dudx=d(x)dxdudx=1

And,

du=1dx …...…..

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