Prove that

L{$Sin{at}$} =$\frac{a} {(s^{2}+a^{2})},s>0$

Prove that

L$Cosat=\frac{s} {s^{2}+a^{2}},s>0$

Prove that ​​​​​​

L{$Sinhat$}$=\frac{a} {s^{2}-a^{2}},s>|a|$​​

Prove that

L{$coshat$} =$\frac{s} {s^{2}-a^{2}},s>|a|$

Find the laplace transformation of

Sin2t cos3t

Find the laplace transformation of$Sin^{3}2t$

Find the laplace transformation of$Cosh^{3}2t$

Find the laplace transformation of$(\sqrt{t} +\frac{1}{\sqrt{t}})^{3}$

Find the laplace transformation of$(1+te^{-t})^{3}$

Find the laplace transformation of$e^{-3t}cos^{2}t$

Find the laplace transformation of$Sinh3tcos^{2} t$