   Chapter 5.3, Problem 46E ### 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 31–46, use any basic integration formula or formulas to find the indefinite integral. State which integration formula(s) you used to find the integral. ∫ x 2 + x + 1 x 2 + 1   d x

To determine

To calculate: The indefinite integral x2+x+1x2+1dx.

Explanation

Given Information:

The provided indefinite integral is x2+x+1x2+1dx.

Formula used:

The general logarithmic rule of integration:

1ududx=ln|u|+C

The constant rule of integration:

cu=u+C

Calculation:

Consider the indefinite integral:

x2+x+1x2+1dx

Rewrite the integrand as:

x2+x+1x2+1dx=(x2+1)+xx2+1dx=(1+xx2+1)dx

Apply, distribution property of integration:

(1+xx2

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