Calculating the Laplace Transform of a Unit Step Function

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1. Determine the Laplace transform of a unit step function u(t) where:
u(t) = 1, for t >= 0
u(t) = 0, for t < 0

I've searched and searched for a solution relating to this problem but could not find anything. Completely forgot how to do an equation like this since it's been a good 3 years since I took my first calculus class. Any help would be appreciated.
 
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What's the definition of the Laplace transform of an arbitrary function f(t)?
 

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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