What is expand 2+U(t-7/2)e^{-t}sin(pit) ?

The solution to expand 2+U(t-7/2)e^{-t}sin(pit) is 2+e^{-t}Utsin(pit)-(7e^{-t}Usin(pit))/2

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expand 2+U(t-7/2)e^{-t}sin(pit)

expand

2 + U (t - \frac{7}{2}) e^{- t} sin (π t)

2 + e^{- t} U t sin (π t) - \frac{7 e ^{- t} U sin ( π t )}{2}

Solution steps

2 + U (t - \frac{7}{2}) e^{- t} sin (π t)

= 2 + e^{- t} U sin (π t) (t - \frac{7}{2})

Expand

U e^{- t} sin (π t) (t - \frac{7}{2}) : e^{- t} U t sin (π t) - \frac{7 e ^{- t} U sin ( π t )}{2}

= 2 + e^{- t} U t sin (π t) - \frac{7 e ^{- t} U sin ( π t )}{2}

\frac{1}{( s + 1 ) ( s + 2 ) \cdot e ^{- 2 s - 2}}

\frac{9 x ^{2} + 3 x + 2}{( x ^{2} - 9 ) x}

\frac{5 x}{2 ( 2 x ^{2} + 1 )}

- e^{- x} x^{2} + 2 (- e^{- x} x - e^{- x})

cos (2 t) U (t - \frac{13 π}{4})

What is expand 2+U(t-7/2)e^{-t}sin(pit) ?
The solution to expand 2+U(t-7/2)e^{-t}sin(pit) is 2+e^{-t}Utsin(pit)-(7e^{-t}Usin(pit))/2