# 1) find the laplace transformation of e^at + b?

$We\; \; know \; \; that\; \; L[{f(t)}]=\int_{0}^{\infty } e^{-st}f(t)dt$

$f(t)=e^{at+b}$

$L[{f(t)}]=\int_{0}^{\infty } e^{-st}e^{at+b}dt$

$L[{f(t)}]=\int_{0}^{\infty } e^{(-s+a)t+b}dt$

$L[{f(t)}]=e^{b}\int_{0}^{\infty } e^{(-s+a)t}dt$

$L[{f(t)}]=\frac{e^{b}}{s-a}\; \; \; \; \; \; \; \; \; \; \; \; (\because \int_{0}^{\infty } e^{(-s+a)t}dt=\frac{1}{s-a})$

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