What is L^{-1}{(e^{-6s})/(s^2+36)}(t) ?

The solution to L^{-1}{(e^{-6s})/(s^2+36)}(t) is (e^{-6s}t)/(L(s^2+36))

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simplify L^{-1}{(e^{-6s})/(s^2+36)}(t)

simplify

L^{- 1} {\frac{e ^{- 6 s}}{s ^{2} + 36}} (t)

\frac{e ^{- 6 s} t}{L ( s ^{2} + 36 )}

Solution steps

L^{- 1} {\frac{e ^{- 6 s}}{s ^{2} + 36}} (t)

Apply exponent rule:

a^{- 1} = \frac{1}{a}

= \frac{1}{L} t {\frac{e ^{- 6 s}}{s ^{2} + 36}}

Remove parentheses:

(a) = a

= \frac{1}{L} \cdot \frac{e ^{- 6 s}}{s ^{2} + 36} t

Multiply fractions:

a \cdot \frac{b}{c} \cdot \frac{d}{e} = \frac{a \cdot b \cdot d}{c \cdot e}

= \frac{1 \cdot e ^{- 6 s} t}{L ( s ^{2} + 36 )}

Multiply:

1 \cdot e^{- 6 s} = e^{- 6 s}

= \frac{e ^{- 6 s} t}{L ( s ^{2} + 36 )}

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What is L^{-1}{(e^{-6s})/(s^2+36)}(t) ?
The solution to L^{-1}{(e^{-6s})/(s^2+36)}(t) is (e^{-6s}t)/(L(s^2+36))