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

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Chapter 5.3, Problem 26E
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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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Using the log Rule for integration In Exercises 13–30, find the indefinite integral. See Examples 4, 5, and 6.

∫ x 2 + 2 x + 3 x 3 + 3 x 2 + 9 x + 1   d x

To determine

To calculate: The indefinite integral ∫x2+2x+3x3+3x2+9x+1dx.

Explanation

Given Information:

The provided indefinite integral is ∫x2+2x+3x3+3x2+9x+1dx

Formula used:

The logarithmic rule of integrals:

∫duu=ln|u|+C

Calculation:

Consider the indefinite integral:

∫x2+2x+3x3+3x2+9x+1dx

Let u=x3+3x2+9x+1, then derivative will be,

du=d(x3+3x2+9x+1)=(3x2+6x+9)dx=3(x2+2x+3)dx

Rewrite the integrand as:

13∫3(x2+2x+3)dxx3+3x2+9x+1

Substitute du for 3(x2+2x+3)dx and u for x3+3x2+9x+1 in provided integration

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