What is e^{-st}*t*(e^{it}+e^{-it}) ?

The solution to e^{-st}*t*(e^{it}+e^{-it}) is 2e^{-st}tcos(t)

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simplify e^{-st}t(e^{it}+e^{-it})

simplify

e^{- s t} \cdot t \cdot (e^{i t} + e^{- i t})

2 e^{- s t} t cos (t)

Solution steps

e^{- s t} t (e^{i t} + e^{- i t})

e^{i t} = cos (t) + i sin (t)

e^{- i t} = cos (t) - i sin (t)

= e^{- s t} t (cos (t) + i sin (t) + cos (t) - i sin (t))

Simplify

cos (t) + sin (t) i + cos (t) - i sin (t) : 2 cos (t)

= 2 e^{- s t} t cos (t)

2 π (\frac{9 π}{4} - 36)

\frac{32 ( x + 1 )}{27}

(3 x^{2} - 5)^{2} d x

x^{2} \cdot x^{1}

(2 u + 1)^{2} d u

What is e^{-st}*t*(e^{it}+e^{-it}) ?
The solution to e^{-st}*t*(e^{it}+e^{-it}) is 2e^{-st}tcos(t)