Need help with partial fractions integral for flux through a cube?

JJfortherear
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Homework Statement



integral of: 1/(((L2)/4)+y2)This is for proving the flux through a cube from a wire going through it is = Qenc/epsilon0

All that's left for one face after taking out constants is the above equation, and I really don't want to go re learn how to do partial fractions again. Any help?
 
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Use a trig substitution, rather than partial fractions.
 
Mark44 said:
Use a trig substitution, rather than partial fractions.

alright, was just waiting for someone to say it :)
 

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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