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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