What is expand e^tsin(t)U(t-pi/2) ?

The solution to expand e^tsin(t)U(t-pi/2) is e^ttUsin(t)-(pie^tUsin(t))/2

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expand e^tsin(t)U(t-pi/2)

expand

e^{t} sin (t) U (t - \frac{π}{2})

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

Solution steps

e^{t} sin (t) U (t - \frac{π}{2})

= e^{t} U sin (t) (t - \frac{π}{2})

Apply the distributive law:

a (b - c) = ab - a c

a = e^{t} sin (t) U, b = t, c = \frac{π}{2}

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

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

Simplify

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

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

\frac{s + 4}{s ( s ^{2} + 4 s + 104 )}

a (e^{b x} + b e^{b x} x)

\frac{x ^{2} + 4}{x ^{2}}

\frac{8 ( 2 - 2 x ) ^{3}}{3}

- 4 (x + 2) - \frac{1}{3} (- 12 x = 3)

What is expand e^tsin(t)U(t-pi/2) ?
The solution to expand e^tsin(t)U(t-pi/2) is e^ttUsin(t)-(pie^tUsin(t))/2