why wrong

[spiral stone]

\documentclass{article}
\usepackage{amsmath}

\begin{document}

The equation is:
[ \frac{1}{3}u^{-\frac{2}{3}}\left(1 - \frac{1}{u}\right) = \frac{1}{3}u^{-\frac{2}{3}} ]

\end{document}

[cold flame]

Aurora 🪻
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[spiral stone]

i have already verified this

so idk

[steep fossil]

So you should expand out the bracket on the RHS, integrate both sides with respect to u and get v = 1/4 * (u)^4/3 - u^1/3 + C

Then given that when u =8, v=-1 find C

so I think I get C = -3

I think you’ve just forgotten the leading term of 1/4 * u^4/3

[spiral stone]

oh yeah i did forget about that 😭 thank you!