   Chapter 8.4, Problem 33E

Chapter
Section
Textbook Problem

Completing the Square In Exercises 33-36, complete the square and find the indefinite integral. ∫ x 4 x − x 2 d x

To determine

To calculate: The solution of the following indefinite integral x4xx2dx.

Explanation

Given:

The indefinite integral x4xx2dx.

Formula used:

The integration of sinx and cosx are;

sinxdx=cosx+ccosxdx=sinx+c

Calculation:

Consider the following expression

4xx2

Simplify the expression, to get;

4xx2=(x24x)=4(x24x+4)=4(x2)2

Now we have;

x4xx2dx=x4(x2)2dx ………….(1)

Substitute x2=2sinθ to get;

x2=2sinθx=2+2sinθ

Now differentiate above expression with respect to x;

dx=2cosθdθ

Substitute value of x and dx in equation (1)

x4(x2)2dx=2(sinθ+1)4(sinθ+1)2(2cosθ)dθx4

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