To determine The relation between differentiation method and integration by substitution and what type of integrand suggests using integration by substitution. Explanation Integration by substitution, also known as u − substitution method is related to the chain rule of differentiation. This can be explained as under, Let f ( x ) = 2 x ( x 2 + 2 ) Integrate this function, ∫ 2 x ( x 2 + 2 ) d x … … ( 1 ) Let ( x 2 + 2 ) = u , then 2 x d x = d u … … ( 2 ) Substitute equation (2) in equation (1) to get, ∫ u d u Integrate this function to get, u 2 2 + C … … ( 3 ) Replace the value of ( x 2 + 2 )

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Chapter 13.2, Problem 1E

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The relation between differentiation method and integration by substitution and what type of integrand suggests using integration by substitution.

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Chapter 13.2, Problem 8CP

Chapter 13.2, Problem 2E

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