Inverse Laplace Transform of (s + 5)/(s² + 2s + 10)
The inverse Laplace transform of (s + 5)/(s² + 2s + 10) is e^(-t)·cos(3t) + 4/3·e^(-t)·sin(3t). See the partial fraction expansion and the transform pair used for each term, then edit F(s) to try your own.
L⁻¹{(s + 5)/(s² + 2s + 10)} = e^(-t)·cos(3t) + 4/3·e^(-t)·sin(3t). Complete the square to read off the damping and the damped frequency.
e.g. 2s+3
Expanded or factored, e.g. (s+1)(s^2+4)
The result
L⁻¹{(s + 5)/(s² + 2s + 10)} = e^(-t)·cos(3t) + 4/3·e^(-t)·sin(3t)
Partial fractions: (s + 5)/(s^2 + 2s + 10)
- Invert (s + 5)/(s^2 + 2s + 10) — L⁻¹{(Bs + C)/((s − a)² + b²)} = e^(at)[B·cos bt + ((C + aB)/b)·sin bt]
Complete the square to read off the damping and the damped frequency.
More inverse transforms
Frequently asked questions
What is the inverse Laplace transform of (s + 5)/(s² + 2s + 10)? ▾
It is f(t) = e^(-t)·cos(3t) + 4/3·e^(-t)·sin(3t). Complete the square to read off the damping and the damped frequency.
What are the partial fractions here? ▾
F(s) splits into (s + 5)/(s^2 + 2s + 10), and each piece is inverted separately.
How can I check this answer? ▾
Transform e^(-t)·cos(3t) + 4/3·e^(-t)·sin(3t) forward again with the Laplace transform calculator — you should get back (s + 5)/(s² + 2s + 10).
About this Calculator
The inverse Laplace transform of (s + 5)/(s² + 2s + 10) is e^(-t)·cos(3t) + 4/3·e^(-t)·sin(3t). See the partial fraction expansion and the transform pair used for each term, then edit F(s) to try your own.