I found this picture on Twitter and I'm curious is it solvable or not. For me, a first-year student with little math knowledge, it is just looks like a mess.

enter image description here

Solve for the password : $$ \frac{ \int u (u^2 +5)^{1/2}~du - 3 \int u (u^2 -5)^{-1/2}~ }{\displaystyle\int \frac{u ((u^2 +5)-3)}{\sqrt{u^2 +5}}~du}$$

  • $\begingroup$ Did you try inputting this formula into Wolfram Alpha? Also attempt substitution on the integrals. $\endgroup$ Oct 8 '19 at 8:04
  • 2
    $\begingroup$ I think the expression is supposed to be $$ \frac{ \int u (u^2 +5)^{1/2}~du - 3 \int u (u^2 -5)^{-1/2}~du }{\int \frac{u ((u^2 +5)-3)}{\sqrt{u^2 +5}}~du} $$ $\endgroup$
    – Matti P.
    Oct 8 '19 at 8:06

No need to know much of calculus,


My bet is that the "Pasword" is "one" or "1", assuming a typo ($-5$ instead of $+5$; also missing $du$), and assuming that the integration constants can be ignored.


It's ridiculous. Numerator and denominator are same, if we more generalise the integration.. So,ans is 1

  • $\begingroup$ Isn't your answer the same as what Yves has written? $\endgroup$
    – Toby Mak
    Oct 8 '19 at 9:36
  • $\begingroup$ Problem lies in the constant of integration $\endgroup$
    – wilsonw
    Oct 8 '19 at 10:08
  • $\begingroup$ They are quasi the same... $\endgroup$
    – user65203
    Oct 8 '19 at 10:30

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