What is (e^{kt}+e^{-kt})e^{-st}dt ?

The solution to (e^{kt}+e^{-kt})e^{-st}dt is e^{-kt-ts}dt(e^{2kt}+1)

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simplify (e^{kt}+e^{-kt})e^{-st}dt

simplify

(e^{k t} + e^{- k t}) e^{- s t} d t

e^{- k t - t s} d t (e^{2 k t} + 1)

Solution steps

(e^{k t} + e^{- k t}) e^{- s t} d t

Apply exponent rule:

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

= \frac{1}{e ^{t s}} (e^{k t} + e^{- k t}) d t

Multiply fractions:

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

= \frac{1 \cdot ( e ^{k t} + e ^{- k t} ) d t}{e ^{s t}}

Multiply:

1 \cdot (e^{k t} + e^{- k t}) = (e^{k t} + e^{- k t})

= \frac{( e ^{k t} + e ^{- k t} ) d t}{e ^{t s}}

Factor

e^{k t} + e^{- k t} : e^{- k t} (e^{2 k t} + 1)

= \frac{e ^{- k t} ( e ^{2 k t} + 1 ) d t}{e ^{s t}}

Cancel

\frac{e ^{- k t} ( e ^{2 k t} + 1 ) d t}{e ^{s t}} : e^{- k t - s t} (e^{2 k t} + 1) d t

= e^{- k t - s t} (e^{2 k t} + 1) d t

= e^{- k t - t s} d t (e^{2 k t} + 1)

1.00497 (10)^{- 6}

(5.1001 \cdot 1 0^{- 8}) 0.25

(1 - x^{16})^{4} (1 - x)^{- 4}

(- 3 x y) e^{2} (- 2 x e^{2} y) e^{3}

2.93 e^{(- 1.8 (0))}

What is (e^{kt}+e^{-kt})e^{-st}dt ?
The solution to (e^{kt}+e^{-kt})e^{-st}dt is e^{-kt-ts}dt(e^{2kt}+1)