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...

Extracted text: 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 a/s((-1/s)e^(-st)*sin(at)) a? 00 1/s e^(-st)cos(at)dt s2 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-st cos(at) dt - Therefore st cos(at) dt s/(a^2+s^2) || ||