Chapter 5.3, Problem 25E

### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

Chapter
Section

### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Using the log Rule for integration In Exercises 13–30, find the indefinite integral. See Examples 4, 5, and 6. ∫ x + 3 x 2 + 6 x + 7   d x

To determine

To calculate: The indefinite integral x+3x2+6x+7dx.

Explanation

Given Information:

The provided indefinite integral is x+3x2+6x+7dx

Formula used:

The logarithmic rule of integrals:

duu=ln|u|+C

Calculation:

Consider the indefinite integral:

x+3x2+6x+7dx

Let u=x2+6x+7, then derivative will be,

du=d(x2+6x+7)=(2x+6)dx=2(x+3)dx

Rewrite the integrand as:

122(x+3)dxx2+6x+7

Substitute du for 2(x+3)dx and u for x2+6x+7 in provided integration

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