   Chapter 5.1, Problem 27E ### 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 indefinite integrals In Exercises 25–36, find the indefinite integral. Check your result by differentiating. See Examples 4 and 5. ∫ ( x 5 − 8 )   d x

To determine

To calculate: The value of indefinite integral (x58)dx and check the result by differentiation.

Explanation

Given Information:

The indefinite integral is (x58)dx.

Formula used:

The simple power rule of integration, xndx=xn+1n+1+C where n1.

The difference rule of integration, (f(x)g(x))dx=f(x)dxg(x)dx.

The simple power rule for the derivative, ddx[xn]=nxn1.

Calculation:

Consider the indefinite integral (x58)dx.

The integrand of the indefinite integral is (x58).

Integrate the provided indefinite integral use the difference rule of integration, (f(x)g(x))dx=f(x)dxg(x)dx.

(x58)dx=x5dx8dx

Now, use the simple power rule of integration, xndx=xn+1n+1+C where n1

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