91Ó°ÊÓ

In Problems 1-20, determine the Laplace transform of the given function using Table 7.1 on page 356 and the properties of the transform given in Table 7.2. [Hint: In Problems 12-20, use an appropriate trigonometric identity.]

${\mathbf{e}}^{\mathbf{-}\mathbf{2}\mathbf{t}}\mathbf{sin}\mathbf{2}\mathbf{t}\mathbf{+}{\mathbf{e}}^{\mathbf{3}\mathbf{t}}{\mathbf{t}}^{\mathbf{2}}$

In Problems 1-20, determine the Laplace transform of the given function using Table 7.1 on page 356 and the properties of the transform given in Table 7.2. [Hint: In Problems 12-20, use an appropriate trigonometric identity.]

$\mathbf{(}\mathbf{t}\mathbf{-}\mathbf{1}{\mathbf{)}}^{\mathbf{4}}$.

In Problems 1-20, determine the Laplace transform of the given function using Table 7.1 on page 356 and the properties of the transform given in Table 7.2. [Hint: In Problems 12-20, use an appropriate trigonometric identity.]

${\left(1+e^{-t}\right)}^{\mathbf{2}}$.

In Problems 1-20, determine the Laplace transform of the given function using Table 7.1 on page 356 and the properties of the transform given in Table 7.2. [Hint: In Problems 12-20, use an appropriate trigonometric identity.]

${\mathbf{e}}^{\mathbf{-}\mathbf{t}}\mathbf{tsin}\mathbf{2}\mathbf{t}$

Determine the inverse Laplace transform of the given function.

$\frac{\mathbf{6}}{{\mathbf{(}\mathbf{s}\mathbf{-}\mathbf{1}\mathbf{)}}^{\mathbf{4}}}$.

Determine the inverse Laplace transform of the given function.

$\frac{\mathbf{s}\mathbf{+}\mathbf{1}}{{\mathbf{s}}^{\mathbf{2}}\mathbf{+}\mathbf{2}\mathbf{s}\mathbf{+}\mathbf{10}}$.

Determine the inverse Laplace transform of the given function.

$\frac{\mathbf{1}}{{\mathbf{s}}^{\mathbf{2}}\mathbf{+}\mathbf{4}\mathbf{s}\mathbf{+}\mathbf{8}}$.

Determine the inverse Laplace transform of the given function.

$\frac{\mathbf{2}\mathbf{s}\mathbf{+}\mathbf{16}}{{\mathbf{s}}^{\mathbf{2}}\mathbf{+}\mathbf{4}\mathbf{s}\mathbf{+}\mathbf{13}}$.

Determine the inverse Laplace transform of the given function.

$\frac{\mathbf{1}}{{\mathbf{s}}^{\mathbf{5}}}$.

In Problems 1-10, determine the inverse Laplace transform of the given function.

$\frac{\mathbf{3}\mathbf{s}\mathbf{-}\mathbf{15}}{\mathbf{2}{\mathbf{s}}^{\mathbf{2}}\mathbf{-}\mathbf{4}\mathbf{s}\mathbf{+}\mathbf{10}}$