00 L{cos}(s) = -st e cos(at) dt u cos(at) dv e^(-st)dt du = -asin(at)du v =| (-1/s)e^(-st) 00 (a/s)e^(-st)sin(at)dt - U = als*sin(at) dv e^(-st)dt du = (a^2/s)*cos(at)dt v = (-1/s)e^(-st) 00 00 1/s als(-1/s)e^(-st)*sin(at)) a? 00 1/s e^(-st)cos(at)dt 82 Notice that this last integral is the same as the integral we started with. Treat this like an equation and move the integral to the left hand side: 1 e-at cos(at) dt - Therefore Je-t cos(at) dt s/(a^2+s^2) || || ||

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