5.3 利用常用函数[例如 (t),(e)^-alpha tg(t), sin(βt)g(t),cos(βt)g(t)等]的象函数及拉普拉斯变换的性质,-|||-求下列函数f(t)的拉普拉斯变换F(s )。-|||-(1) ^-tg(t)-(e)^-(t-2)g(t-2)-|||-(2) ^-t[ g(t)-g(t-2)] -|||-(3) sin (pi t)[ g(t)-g(t-1)] -|||-(4) sin (pi t)g(t)-sin [ pi (t-1)] g(t-1)-|||-(5) 8(4t-2)-|||-(6) cos (3t-2)g(3t-2)-|||-(7) sin (2t-dfrac (pi )(4))g(t)-|||-(8) sin (2t-dfrac (pi )(4))in (2t-dfrac (pi )(4))-|||-(9) (int )_(0)^1sin (pi x)dx-|||-(10) (int )_(0)^x(int )_(0)^pi sin (pi x)dxcdot dpi -|||-(11) dfrac ({d)^2}(d{t)^2}[ sin (pi t)g(t)] -|||-(12) dfrac ({d)^2sin (pi t)}({d)^2}g(t)-|||-(13) ^2(e)^-2tg(t)-|||-(14)(t)^2cos tin (t)-|||-(15) ^-(t-3)g(t-1)-|||-(16) ^-alpha cos (beta t)g(t)