Find the laplace transform of the following 1) SHIFTING f(t)=(1+te^{-t})^3

he298c 2020-12-22 Answered
Find the laplace transform of the following
1) SHIFTING
f(t)=(1+tet)3
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Expert Answer

insonsipthinye
Answered 2020-12-23 Author has 83 answers
Step 1
Simplify:
f(t)=(1+tet)3
=1+3tet+3t2e2t+t3e3t
Step 2
Calculate Laplace transform of eat:
0eatestdt=0e(s+a)tdt
=1(s+a)
Step 3 Thus, Laplace transform of tneat is:
(1)ndndsn(1(s+a))=(1)ndndsn(s+a)1
=(n!)(s+a)n+1
Step 4 Therefore Laplace transform of f(t)=1+3tet+3t2e2t+t3e3t is: 
(0!)(s+0)0+1+(31!)(s+1)1+1+(32!)(s+2)2+1+(3!)(s+3)3+1=1s+3(s+1)2+6(s+2)3+6(s+3)4
Step 5
Therefore Laplace transform of f(t) is 1s+3(s+1)2+6(s+2)3+6(s+3)4
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