Explanation Given: The provided expression is ∫ 3 x 3 + 4 x ( x 2 + 1 ) 2 d x . Formula used: ∫ 1 a d a = ln a Calculation: Let, I = ∫ 3 x 3 + 4 x ( x 2 + 1 ) 2 d x I = ∫ x ( 3 x 2 + 4 ) ( x 2 + 1 ) 2 d x Put x 2 = t On differentiating both sides, 2 x d x = d t On substituting, I = 1 2 ∫ ( 3 t + 4 ) ( t + 1 ) 2 d t = 3 2 ∫ t ( t + 1 ) 2 d t + 2 ∫ d t ( t + 1 ) 2 = I 1 − 2 t + 1 + C Therefore I 1 = 3 2 ∫ t

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Author: Larson

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Chapter 8, Problem 62RE

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To calculate: The value of the indefinite integral ∫3x3+4x(x2+1)2dx.

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Chapter 8, Problem 61RE

Chapter 8, Problem 63RE

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Chapter 8 Solutions

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The value of the indefinite integral ∫ 3 x 3 + 4 x ( x 2 + 1 ) 2 d x .

Solution Summary: The author explains how to calculate the value of the indefinite integral, which is underset, and 2xdx=dt.

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To calculate: The value of the indefinite integral ∫3x3+4x(x2+1)2dx.

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Chapter 8 Solutions