What is t^3e^tcos(4t)e^{-t} ?

The solution to t^3e^tcos(4t)e^{-t} is t^3cos(4t)

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simplify t^3e^tcos(4t)e^{-t}

simplify

t^{3} e^{t} cos (4 t) e^{- t}

t^{3} cos (4 t)

Solution steps

t^{3} e^{t} cos (4 t) e^{- t}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{t} e^{- t} = e^{t - t}

= t^{3} cos (4 t) e^{t - t}

Add similar elements:

t - t = 0

= t^{3} cos (4 t) e^{0}

Apply rule

a^{0} = 1, a \neq = 0

e^{0} = 1

= 1 \cdot t^{3} cos (4 t)

Multiply:

cos (4 t) \cdot 1 = cos (4 t)

= t^{3} cos (4 t)

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