find the inverse laplace transform of (s+4)/(s(s-1)(s^2+4))
You asked:
Find the inverse laplace transform of \(\frac{s + 4}{s \cdot \left(s - 1\right) \cdot \left({s}^{2} + 4\right)}\)
MathBot Answer:
\[\mathcal{L}_{s}^{-1}\left\{\frac{s + 4}{s \left(s^{2} + 4\right) \left(s - 1\right)}\right\}(t) = \frac{\left(2 e^{t} - \sin{\left(2 t \right)} - 2\right) \theta\left(t\right)}{2}\]
$e$ is Euler's number, a mathematical constant that is approximately $2.71828$.
$\theta$ is the Heaviside function.