# Solving equation for wifi password.

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.

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

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

No need to know much of calculus,

$$\frac{u((u^2+5)-3)}{\sqrt{u^2+5}}=u(u^2+5)^{1/2}-3u(u^2+5)^{-1/2}.$$

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

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