How to Perform Inverse Laplace Transform for 1/(s+a)^n?

tony873004
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How do I do the inverse of this? 1/(s+a)n is not in the table.

\begin{array}{l}<br /> Y\left( s \right) = \frac{1}{{\left( {s + 4} \right)^4 }} \\ <br /> y\left( t \right) = L^{ - 1} \left[ {Y\left( s \right)} \right] \\ <br /> \end{array}
 
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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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