   Chapter 5.3, Problem 8QY ### 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
1 views

# In Exercises 1-9, find the indefinite integral. Check your result by differentiating. ∫ 4 x 2 ( x 3 + 3 ) 3   d x

To determine

To calculate: The indefinite integral 4x2(x3+3)3dx.

Explanation

Given Information:

The provided indefinite integral is 4x2(x3+3)3dx.

Formula used:

The power rule of integrals:

undu=xn+1n+1+C (for n1)

The power rule of differentiation:

dduun=nun1+C

Calculation:

Consider the indefinite integral:

4x2(x3+3)3dx

Let u=x3+3, then derivative will be,

du=d(x3+3)=3x2dx

Rewrite above indefinite integration as:

433x2dx(x3+3)3

Substitute du for 3x2dx and u for x3+3 in provided integration.

433x2dx(x3+3)3=43duu3=43u3du

Now apply, the

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