L[f(x)] = f(s) = 0∫∞ e-sx f(x) dx
L[xn] = n! / s n+1
L[f n (x)] = s n L(f(x) - s n-1 f(0) - s n-2 f 1(0)
L[c] = c/s
L[sinat] = a / (s2 + a2)
L[cosat] = s / (s2 + a2)
L[sinhat] = a / (s2 - a2)
L[coshat] = s / (s2 - a2)
L[t sinat] = 2as / (s2 + a2) 2
L[t cosat] = (s2 - a2) / (s2 + a2) 2
L[eat] = 1 / (s-a)
L[e-at] = 1 / (s+a)
L[tn] = n! / sn+1
L[tn eat] = n! / (s-a) n+1
L[f(x-a) * u(x-a)] = e-as F(S)
L[√x]
= √∏ / 2s3/2
Inverse
Laplace Transform
L-1[c/s] = c where c is a constant
L-1[a / (s2 + a2)] = sinat
L-1[s / (s2 + a2)] = cosat
L-1[a / (s2 - a2)] = sinhat
L-1[s / (s2 - a2)] = coshat
L-1[2as / (s2 + a2) 2] = t sinat
L-1[(s2 - a2) / (s2 + a2) 2] = t cosat
L-1[1 / (s-a)] = eat
L-1[1 / (s+a)] = e-at
L-1[n! / sn+1] = tn
L-1[n! / (s-a) n+1] = tn eat
L-1[√∏ / 2s3/2] = √x
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