How Can I Convert Maple Input into LaTeX for the Intermediate Value Theorem?

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I typed this in maple and I could not convert it into latex. I included line numbering in the pdf. If u need to quote just quote the line numbers. Sorry for any inconvenience caused.

http://dl046.filefactory.com/cache/dl/f/7207eb//b/6/h/1de51f5dd9ec236e54e5da7d/n/Intermediate_Value_Theorem.pdf

I try to do this question but I am not really what the question want. I will appreciate if anyone can tell me my mistakes. Thanks.
 
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I'm not going to sign up for "file factory" whatever simply to look at a PDF file. Please try typing the latex form of your question, or provide explanation some other way.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

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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