I am away from Laplace transform for years, and now I have to solve $$\mathcal{L}^{-1} \left\{ s^{-\frac32}\sqrt{\frac{as+b}{cs+b}} \right\}(t),$$ where $a,b,c$ are real positive numbers. I can find inverse Laplace for $s^{-k}$ but really I got stuck on this. Please guide me to solve this form. Thanks in advance. Implicitly it has the condition $\lim\limits_{s\to\infty}F(s)=0$
Honestly I don't know what should I do for $\sqrt{\frac{as+b}{cs+b}}$.
2026-04-23 21:11:26.1776978686
Inverse Laplace Transform hint
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