Use a variable substitution to get into a Bessel equation form?

ipat918
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Homework Statement
Use a variable substitution to get into a Bessel equation form?
Relevant Equations
Bessel equation
Hello,

For my homework I am supposed to get-
242729

into the form of a Bessel equation using variable substitution. I am just not sure what substitution to use.
Thanks in advance.
 

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Forum rules require you to show your efforts at finding a solution. Also, please state the entire problem as given.
 
Hello,

I apologize, I didn't read the rules properly beforehand. The question is part of a much longer, complex question, this is just the part I am stuck on and it is literally all the information I have to solve it. As for my efforts, well there are none right now. I have no idea where to even start on guessing what substitution to use.

Thanks
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...

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