Evaluating an Integral With Constant C & E

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I need to evaluate the integral of:

1/(E-Cx^4)^(1/2) from x0 to x.


Both C and E are constants.


I've been looking for an appropriate substitution or maybe something along the lines of inverse trigonometric substitution but everything I think of runs into a dead end.

Help would be much appreciated.
 
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What do you know about elliptic integrals of the first kind?
Because doing your integral with Mathematica gives me one in the result.
 

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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