22. PROJECT. Further Results by Differentiation.Proceeding as in Example 1, obtain \text { (a) } \mathscr{I}(t \cos \omega t)=\frac{s^{2}-\omega^{2}}{\left(s^{2}+\omega^{2}\right)^{2}} and from this and Example 1: (b) formula 21, (c) 22,(d)

23 in Sec. 6.9. \text { (e) } \mathscr{L}(t \cosh a t)=\frac{s^{2}+a^{2}}{\left(s^{2}-a^{2}\right)^{2}} \text { (f) } \mathscr{L}(t \sinh a t)=\frac{2 a s}{\left(s^{2}-a^{2}\right)^{2}}