Proving Convergence or Divergence of (k^1/2)*(ln k )/(k^3 +1)

raycao88124 · 2008-07-27T21:40:38+00:00

(k^1/2)*(ln k )/(k^3 +1) how to prove it con or div? i tried comparison, limit comparison, etc... but just don't know how to prove it.. please help...

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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Proving Convergence or Divergence of (k^1/2)*(ln k )/(k^3 +1) - Help Needed

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

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