Probably a trivial question but I can't understand how to argue away the value of integrals in complex analysis. I am trying to find the inverse Laplace transform of $F(s)=\frac{1}{s(s+1)}$. The integral I therefore have to compute is $f(t)=\dfrac{1}{2\pi i}\int^{c+i\infty}_{c-i\infty}\dfrac{e^{st}}{s(s+1)}ds$ and I'm using the 'Bromwich contour'. I have to 'argue away' the contribution from the semi-circular arc of the 'Bromwich contour' but I don't understand the method of how to do so.$$|\int_c|\leq2\pi R.max\dfrac{e^{st}}{s(s+1)}$$ any help in understanding the method would be appreciated.
2026-03-28 03:51:39.1774669899
arguing away - complex analysis
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Hint: On the arc and assuming $t>0$, $|e^{st}|\leq e^{ct}$ and $\max \left|s^{-1}(s+1)^{-1}\right| \sim R^{-2}$ as $R \to \infty$.