   Chapter 5.1, Problem 26E ### 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. ∫ ( 5 − x )   d x

To determine

To calculate: The indefinite integral (5x)dx and verify the result by differentiation.

Explanation

Given Information:

The provided indefinite integral is (5x)dx.

Formula used:

The integration and differentiation formulae used are:

1. ddx[(f(x)±g(x))]=f(x)+g(x)

2. k dx=kx+ C

3. xn dx=xn+1n+1+ C

4. ddx[kx]=k

5. ddx[xn]=nxn1

Here, C is the constant of integration.

Calculation:

Consider the indefinite integral (5x)dx.

Hence,

(5x)dx=5dxxdx

Now, use the formulae k dx=kx+C and xn dx=xn+1n+1+C to evaluate the integral as:

(5x)dx=5dxxdx=5x[x1+12]+C=5xx22+C

Thus, the indefinite integral is evaluated as 5xx22+C

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