What is expand (5t+e^{(-2t)}cos(7t))u(t) ?

The solution to expand (5t+e^{(-2t)}cos(7t))u(t) is 5t^2u+e^{-2t}tucos(7t)

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expand (5t+e^{(-2t)}cos(7t))u(t)

expand

(5 t + e^{(- 2 t)} cos (7 t)) u (t)

5 t^{2} u + e^{- 2 t} t u cos (7 t)

Solution steps

(5 t + e^{(- 2 t)} cos (7 t)) u (t)

= (t) u (5 t + e^{(- 2 t)} cos (7 t))

Apply the distributive law:

a (b + c) = ab + a c

a = u (t), b = 5 t, c = e^{(- 2 t)} cos (7 t)

= u (t) \cdot 5 t + u (t) e^{(- 2 t)} cos (7 t)

= 5 (t) t u + e^{(- 2 t)} (t) u cos (7 t)

Simplify

5 (t) t u + e^{(- 2 t)} (t) u cos (7 t) : 5 t^{2} u + e^{- 2 t} t u cos (7 t)

= 5 t^{2} u + e^{- 2 t} t u cos (7 t)

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\frac{75 ( x - 8 ) ^{2}}{2}

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What is expand (5t+e^{(-2t)}cos(7t))u(t) ?
The solution to expand (5t+e^{(-2t)}cos(7t))u(t) is 5t^2u+e^{-2t}tucos(7t)