Algebra question (irreducibility of polynomial)

nicolep · 2007-11-25T22:23:29+00:00

Homework Statement Show that this polynomial is irreducible over Q[x] Homework Equations x^4 + 6x^3 + 14x^2 + 16x + 9 The Attempt at a Solution I think Eisenstein's criterion will have to be used. But is some substitution to be made?? Please help! Thanks

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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Homework Statement

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The Attempt at a Solution

Thread 'Prove that the integral is equal to ##\pi^2/8##'

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