Explanation Formula used: Indefinite Integral using the Sine and Cosine Function: 1. ∫ sin x d x = − cos x + C 2. ∫ cos x d x = sin x + C Calculation: Obtain the value of the integral ∫ ( x + 1 ) sin ( x 2 + 2 x ) d x as follows. Let u = x 2 + 2 x ; then d u = 2 ( x + 1 ) d x . Substitute u = x 2 + 2 x in the given integral and rewrite it as, ∫ ( x + 1 ) sin ( x 2 + 2 x ) d x = 1 2 ∫ sin ( u ) d u . Use the indefinite integral using the sine and cosine function and obtain the value of the integral as follows. ∫ ( x + 1 ) sin ( x 2 + 2 x ) d x = 1 2 ∫ sin ( u ) d u

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Author: Barnett

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Chapter 8.4, Problem 18E

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To find: The value of the indefinite integral ∫(x+1)sin(x2+2x) dx.

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Chapter 8.4, Problem 17E

Chapter 8.4, Problem 19E

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The value of the indefinite integral ∫ ( x + 1 ) sin ( x 2 + 2 x ) d x .

Solution Summary: The author explains how to obtain the value of the indefinite integral using the sine and cosine function.

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To find: The value of the indefinite integral ∫(x+1)sin(x2+2x) dx.

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Chapter 8 Solutions