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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 5.2, Problem 10E
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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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Applying the General Power Rule In Exercises 9-34, find the indefinite integral. Check your result by differentiating. See Examples 1, 2, 3, and 5.

∫ ( x  - 3 ) 5 / 2   d x

To determine

To calculate: The value of the provided indefinite integral ∫(x−3)52dx.

Explanation

Given Information:

The provided indefinite integral is ∫(x−3)52dx.

Formula Used:

According to the general power rule for integration,

If u is a differentiable function of x, then

∫undu=un+1n+1+C,

where n≠−1

Calculation:

Consider the indefinite integral say I,

I=∫(x−3)52dx

Let

x−3=u … (1)

Differentiate the above equation with respect to x;

ddx(x−3)=dudxddx(x)−ddx(3)=dudx1=dudx

Or

dx=du … (2)

Substitute the values of x−3 and dx from equations (1) and (2) respectively in the provided integral;

I=∫u52du

Now, apply the general power rule for integrtion in the above integral;

I=(u52</

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