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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 3 d x

To determine

To calculate: The value of indefinite integral xx3dx.

Explanation

Given Information:

The provided indefinite integral is xx3dx.

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 xx3dx

Here,

dv=(x3)12dx and u=x

First find v,

dv=(x3)12dxdv=(x3)12dx

On further solving,

v=23(x3)32 …...…... (1)

Now find du,

u=x

Differentiate both side with respect x,

dudx=d(x)dxdudx=1

And,

du=1dx …...…... (2)

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

xx3dx=23x(x3)3223(x3)32dx

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

xx3dx=23x(x3)

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