What is expand (c+1)te^{bt}sin(at) ?

The solution to expand (c+1)te^{bt}sin(at) is ce^{bt}tsin(at)+e^{bt}tsin(at)

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expand (c+1)te^{bt}sin(at)

expand

(c + 1) t e^{b t} sin (a t)

c e^{b t} t sin (a t) + e^{b t} t sin (a t)

Solution steps

(c + 1) t e^{b t} sin (a t)

= e^{b t} t sin (a t) (c + 1)

Apply the distributive law:

a (b + c) = ab + a c

a = t e^{b t} sin (a t), b = c, c = 1

= t e^{b t} sin (a t) c + t e^{b t} sin (a t) \cdot 1

= c e^{b t} t sin (a t) + 1 \cdot e^{b t} t sin (a t)

Multiply:

1 \cdot e^{b t} = e^{b t}

= c e^{b t} t sin (a t) + e^{b t} t sin (a t)

(\frac{1}{x - 3}) + (\frac{1}{x ( x - 3 )})

\frac{( x - 8 ) ( x + 6 ) ( x + 7 )}{4 x ( x - 4 ) ^{2}}

\frac{( 3 n + 1 ) ( 3 n + 2 )}{( 3 n + 4 ) ( 3 n + 5 )}

(x y + y^{2} + x^{2}) d x - x^{2} d y

\frac{4 ( x + 1 )}{( 4 x + 5 )}

What is expand (c+1)te^{bt}sin(at) ?
The solution to expand (c+1)te^{bt}sin(at) is ce^{bt}tsin(at)+e^{bt}tsin(at)