inverse laplace 1/(s+1) — step-by-step solution

Find the causal inverse transform, for t ≥ 0. By linearity, invert each partial fraction

The inverse Laplace formula for

\frac{1}{{(s - a)}^{n}}

t^{n - 1} \cdot \frac{\exp (a t)}{(n - 1)!}

; it gives for

\frac{1}{s + 1}

\frac{\exp (-1 \cdot t)}{0!}

⇥ⓘ Multiplying by -1 gives the opposite:

-1 \cdot t

- t

■By convention, the factorial of 0 is 1:

0!

1

⇥

\frac{\exp (- t)}{1}

ⓘ The factor is moved to the numerator or the denominator by changing the sign of its exponent, for a nonzero base:

\exp (- t)

\frac{1}{\exp (t)}

▶Inverse Laplace transform:

\frac{1}{\exp (t)}