Use integration by parts to find the Laplace transform of the given function f(t)=4tcos h(at)

ka1leE 2020-10-31 Answered
Use integration by parts to find the Laplace transform of the given function
f(t)=4tcosh(at)
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Expert Answer

Fatema Sutton
Answered 2020-11-01 Author has 88 answers
Step 1
Given function is
f(t)=4tcosh(at)
We have to find Laplace transformation by integration by part.
Step 2
So Laplace Transformation is
Lf(t)=40tcosh(at)estdt
 Lf(t)=40t(eat+eat2)estdt
 Lf(t)=20t(e(as)t+e(a+s)t)dt
 Lf(t)=20te(as)tdt+20te(a+s)tdt
 Lf(t)=2[te(as)tsae(as)t(sa)2]0+2[te(a+s)ts+ae(a+s)t(s+a)2]0
 Lf(t)=2[01(sa)2]2[01(s+a)2]
 Lf(t)=2(sa)2+2(s+a)2
 Lf(t)=2(2s2+2a2+2as2as)(sa)2(s+a)2
 Lf(t)=4(s2+a2)(s2a2)2
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