How to manipulate this expression?

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Saladsamurai
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After solving a DE by Laplace I was left with

\frac{1}{s^3}

Now I have a formula for \frac{n!}{s^{n+1}}

which could be \frac{2}{s^{2+1}}

Now if I just multiply the \frac{2}{s^{2+1}}

by a factor of 1/2, is that the same same as my original?

Sorry if this is a stupid question.
 
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Yes.
And I think someone once said that there are no stupid questions.
Cheers.
 
Ssssssweeeeeetttt!

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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