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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Evaluate the indefinite integral. Illustrate and check that your answer is reasonable by graphing both the function and its antiderivative (take C = 0).

x ( x 2 1 ) 3 d x

To determine

To evaluate: The indefinite integral x(x21)3dx.

Explanation

The Indefinite integral is x(x21)3dx.

Let u=x21.

Differentiate on both sides of the above equation as,

du=2xdx12du=xdx

Substitute u for (x21) and (12du) for xdx in x(x21)3dx as,

x(x21)3dx=u3(12du)=12u3du (1)

Integrate the above equation as,

12u3du=12(u3+13+1)+C=12(u44)+C=18u4+C

Thus, the equation (1) becomes,

x(x21)3dx=18u4+C

Substitute (x21) for u in the above equation as,

18u4+C=18(x21)4+C

Thus, the value of the indefinite integral is 18(x21)4+C

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