   Chapter 5.3, Problem 44E ### 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 3 − 36 x + 3 x + 6   d x

To determine

To calculate: The indefinite integral x336x+3x+6dx.

Explanation

Given Information:

The provided indefinite integral is x336x+3x+6dx.

Formula used:

The logarithmic rule of integrals:

duu=ln|u|+C

The power rule of integration:

undu=un+1n+1+C

The constant rule of integration:

cdu=cu+C

Calculation:

Consider the indefinite integral:

x336x+3x+6dx

Rewrite the integrand as:

x336x+3x+6dx=x3+6x26x236x+3x+6dx=x2(x+6)6x(x+6)+3x+6dx=(x+6)(x26x)+3x+6dx=(

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