Help Needed: Solving Logarithmic Equation

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jhen
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hello..

i don't know where to start solving this problem can you please help me?

log phi of x (v)= e-2vx^(1+v/sq.rt.x)2x-1.
please..I really need your help.

Thank you so much.
 
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I don't see a "problem". You have posted an equation. What do you want to do with it?

You titled this "Taylor's series" but of what function? And with respect to what variable, x or v? Or both?
 
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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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