# Calculus-HELP!!!

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Find the Laplace transform of:
f(t) = cos^(2)(2t)

• Calculus-HELP!!! -

cos^2(2t)

L{cos(t)} = s/(s^2+1)
L{f(at)} = 1/a f(s/a), so
L{cos(4t)} = 1/4 (s/4)/(s^2/16+1) = s/(s^2+6)

L{cos^2(2t)} = L{(1+cos(4t))/2}
= 1/2 (L{1} + L{cos(4t)})
= 1/2 (1/s + s/(s^2+16))
= (s^2+8) / (s^3+16s)

• Calculus-HELP!!! -

Thank you!!

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