5.3 利用常用函数[例如 (t),(e)^-atg(t) ,sin(βt)ε(t),cos (βt)ε(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) ^-1g(t)-(e)^-(t-2)g(t-2)-|||-(2) ^-1[ g(t)-e(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) (4t-2)-|||-(6) cos (3t-2)g(3t-2)-|||-(7) sin (2t-dfrac (pi )(4))in (t)-|||-(8) sin (2t-dfrac (pi )(4))in (2t-dfrac (pi )(4))-|||-(9) (int )_(0)^1sin (pi x)dx-|||-(10) (int )_(0)^1(int )_(0)^tsin (pi x)dxcdot dt-|||-(11) dfrac ({d)^2}(d{t)^2}[ sin (pi t)g(t)] -|||-(12) dfrac ({d)^2sin (pi t)}(d{t)^2}g(t)-|||-(13) ^2(e)^-2tg(t)-|||-(14)t^2cos te(t)-|||-(15) (e)^-(t-3)e(t-1)-|||-(16) (e)^-alpha tcos (beta t)in (t)