Find an antiderivative of the function Let u : <mrow class="MJX-TeXAtom-ORD"> <mi ma

Jayla Christensen

Jayla Christensen

Answered question

2022-06-26

Find an antiderivative of the function
Let u : R R be a function. Find an antiderivative of u 2 u in terms of u and its derivatives.
Note: I know an antiderivative of uu′′′ is u u u 2 2 . However it seems for this problem one needs to evaualate antiderivative of either uu′u′′ or u 3 which can't be computed easily via integration by parts

Answer & Explanation

Cristian Hamilton

Cristian Hamilton

Beginner2022-06-27Added 23 answers

Explanation:
Assuming the independent variable t and integrating by parts twice with letting the derivable function to be u 2 ( t ) in first integration and u(t) in the second one, we get u 2 ( t ) u ( t ) u ( t ) u 2 ( t ) + u 3 ( t ) d t .

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