So I'm going to give you two links to imgur, one is the question and the other the answer.

I know how he gets the answer, i can get the answer myself but i have a question..

Do we ALWAYS integrate Euler's equation to use it? OR is this a special case where it gets integrated? If so, what happens when it doesn't get integrated, is a gradient needed?

Thanks

https://imgur.com/a/CHaQCia

https://imgur.com/a/C7YgXrn (Click to zoom)