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tcos-3-t-find-laplace-transform-




Question Number 129308 by BHOOPENDRA last updated on 14/Jan/21
tcos^3 t find laplace transform?
tcos3tfindlaplacetransform?
Answered by Dwaipayan Shikari last updated on 14/Jan/21
L(t cos^3 t)=(1/8)∫_0 ^∞ t e^(−st) (e^(3it) +e^(−3it) +3e^(it) +3e^(−it) )dt                      = (1/8)Γ(2)((1/((s−3i)^2 ))+(1/((s+3i)^2 ))+(3/((s+i)^2 ))+(3/((s−i)^2 )))  =(1/8)(((2(s^2 −9))/((s^2 +9)^2 ))+((6(s^2 −1))/((s^2 +1)^2 )))=((s^2 −9)/(4(s^2 +9)^2 ))+(3/4).((s^2 −1)/((s^2 +1)^2 ))
L(tcos3t)=180test(e3it+e3it+3eit+3eit)dt=18Γ(2)(1(s3i)2+1(s+3i)2+3(s+i)2+3(si)2)=18(2(s29)(s2+9)2+6(s21)(s2+1)2)=s294(s2+9)2+34.s21(s2+1)2

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