Don't forget the +C

Calculus Level 3

Paloma gave her Calculus class a very short math test. This is the dialogue between Paloma and one of her students.

Paloma:\color{#D61F06}{\text{Paloma:}} This test is simple. Find the integral.

(Paloma\color{#D61F06}{\text{Paloma}} writes this integral on the whiteboard) 0lnN4e2u(e2u1)9du dx\int\int_0^{\ln N}\dfrac{4e^{2u}(e^{2u}-1)}{9}du\text{ }dx Ryan:\color{#3D99F6}{\text{Ryan:}} I have no idea how to do this. I can't even come up with a reasonable guess. Maybe I can be smart and get some\textit{some} credit.

(Ryan\color{#3D99F6}{\text{Ryan}} writes on his paper) Let xx be the answer to this question. xx

Paloma:\color{#D61F06}{\text{Paloma:}} Wrong! You forgot the +C+C!

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Problem\underline{\text{Problem}}

What is the NN Paloma wrote in the upper bound that made the answer to the question x+Cx+C?

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Author's note: I know that double integrals are supposed to be definite and have functions in two variables. However, coming up with math jokes is hard.

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