What is inverse oflaplace 7/(s^5) ?

The answer to inverse oflaplace 7/(s^5) is (7t^4)/(24)

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inverse oflaplace 7/(s^5)

inverse laplace

\frac{7}{s ^{5}}

\frac{7 t ^{4}}{24}

Solution steps

L^{- 1} {\frac{7}{s ^{5}}}

= L^{- 1} {\frac{7}{24} \cdot \frac{24}{s ^{5}}}

Use the constant multiplication property of Inverse Laplace Transform:

For function

f (t)

and constant

a : L^{- 1} {a \cdot f (t)} = a \cdot L^{- 1} {f (t)}

= \frac{7}{24} L^{- 1} {\frac{24}{s ^{5}}}

Use Inverse Laplace Transform table:

L^{- 1} {\frac{( n ) !}{s ^{n + 1}}} = t^{n}

L^{- 1} {\frac{24}{s ^{5}}} = t^{4}

= \frac{7}{24} t^{4}

= \frac{7 t ^{4}}{24}

\int \frac{x ^{2}}{( a ^{2} - x ^{2} ) ^{\frac{3}{2}}} d x

x \to 0 lim (x I n x)

(4 sin (2 x))^{^{'}}

\int 3 x^{2} \cdot e^{x^{3}} d x

e^{y} y^{^{'}} = e^{y} + 5 x, y (3) = 7

What is inverse oflaplace 7/(s^5) ?
The answer to inverse oflaplace 7/(s^5) is (7t^4)/(24)