   Chapter 8.4, Problem 28E ### Calculus of a Single Variable

11th Edition
Ron Larson + 1 other
ISBN: 9781337275361

#### Solutions

Chapter
Section ### Calculus of a Single Variable

11th Edition
Ron Larson + 1 other
ISBN: 9781337275361
Textbook Problem

# Finding an Indefinite Integral In Exercises 19-32, find the indefinite integral. ∫ 1 − x x   d x

To determine

To calculate: The solution of the indefinite integral 1xxdx.

Explanation

Given:

The indefinite integral is 1xxdx.

Formula used:

The trigonometric identity, cos2θ=1sin2θ and cos2θ=1+cos2θ2.

The integral identity cosθdθ=sinθ+C.

Calculation:

Because 12x2 is of the form a2x2. So, make use of the trigonometric solution, x=sinθ to solve it as shown in figure.

Differentiate the above equation is;

12xdx=cosθdθ

Therefore;

1xxdx=21sin2θcosθdθ=2cos2θdθ=1+cos2θdθ=(θ+sin2θ2

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