Inverse Laplace transform of $\tan ^{-1} (2/s)$

Question

i am trying to compute inverse Laplace transform of function = $\tan ^{-1} (2/s)$

Answer 1

Hint: $$\mathcal{L}(tf(t))=-\frac{d}{ds}(F(s)).$$

Answer 2

‎$${\cal L}\Big(\frac{\sin2t}{t}\Big)=\int_s^\infty\frac{2}{s^2+4}~ds=\arctan\frac{s}{2}\Big|_s^\infty=\frac{\pi}{2}-\arctan\frac{s}{2}=\arctan\frac{2}{s}$$