In this question, you will use a substitution to carry out the following integration: [ (x² +1)³ 4x³ dx If the answer requires a constant of integration, enter it as c. 5 a. The integral involves the composite function (x² + 1)³ What u-substitution will simplify this term? u = g(x) = du b. Find the derivative dx : du dx 1 c. Transform the original integral into one involving u by using the substitution rule: o Replace all occurrences of 9 (x) in the integral by u. du [6 -dx Replace 9 (x) dx by du (equivalently: replace da Ⓒ (x² +1)5 4x³ dx ² S (x² +1)³ 4x³ dx du (you do not need to enter du in your answer) d. Carry out the integration, and find the most general antiderivative (in terms of u). antiderivative : e. Finally, rewrite your answer in terms of x by replacing u by g(x). [ = by du). ✪

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