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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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