Laplace Transform: Solving Hi Everyone - Help Needed

hedipaldi
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Hi everybody,
can somewone tell me where am i wrong in this solution?(attached here)
thank's
 

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hedipaldi said:
Hi everybody,
can somewone tell me where am i wrong in this solution?(attached here)
thank's

Well, if e^t \longrightarrow 1/(s-1), then e^{t+1} \longrightarrow e/(s-1), not e^s /(s-1).

RGV
 
thank's a lot
 

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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