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)

(x^{3} + \frac{3}{x})^{8}

\frac{10 x + 6}{( x - 3 ) ( x + 3 )}

\frac{s ^{2} ( s + 3 )}{- 3 s ^{3} - 7 s ^{2} + 9 s + 6}

(x + y) d x + x d y

(- 7 x - 2 y = - 1, 3) (x - 2 y = 11)

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)