Prove Idntity - Dirac Delta - Distributions

Drazick
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Homework Statement


The Identity to prove:
vid7j7.png


Homework Equations


Using Integration by parts



The Attempt at a Solution


I couldn't produce the denominator.
 
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Hi Drazic, welcome to PF!:smile:

Drazick said:

Homework Statement


The Identity to prove:
vid7j7.png


Homework Equations


Using Integration by parts



The Attempt at a Solution


I couldn't produce the denominator.

Post your calculations, and we'll be able to help.
 
I solved more general identity.
I'll post it later.
 

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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