How Do You Solve Complex Integrals Using the Error Function?

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I have this question that I have been stuck on for quite sometime. If someone could assist me in solving it then that would be great. Can someone please shed some light?

I have attached the question in a document.

Thankyou
 

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What have you tried to do on this problem?
 
To get started insert the integral definition of the error function into the integral you are doing. View this as a double integral over an area in u,x space. Then look at different ways to evaluate this double integral.
 

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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