Question #345688

Calculate the Laplace transform of

• (t) integral from (0 to t) (T)e^(T)dT


1
Expert's answer
2022-06-01T02:50:42-0400
L{f}(s)=0f(t)estdt{\cal L}\{f\}(s)=\int_0^{\infty}f(t)e^{-st}dtL{t0tTeTdT}(s)=0t0tTeTdTestdt{\cal L}\{t\int_0^tTe^TdT\}(s)=\int_0^{\infty}t\int_0^tTe^TdTe^{-st}dt=0t(1+et(t1))estdt=3s1s2(s1)3=\int_0^{\infty}t(1+e^t(t-1))e^{-st}dt=\frac{3s-1}{s^2(s-1)^3}

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