What is laplacetransform e^3e^t(-sin(pit)) ?

The answer to laplacetransform e^3e^t(-sin(pit)) is e^3-pi/((s-1)^2+pi^2)

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laplacetransform e^3e^t(-sin(pit))

laplace transform

e^{3} e^{t} (- sin (π t))

e^{3} - \frac{π}{( s - 1 ) ^{2} + π ^{2}}

Solution steps

L {e^{3} e^{t} (- sin (π t))}

Use the constant multiplication property of Laplace Transform:

For function

f (t)

and constant

a : L {a \cdot f (t)} = a \cdot L {f (t)}

= e^{3} - 1 L {e^{t} sin (π t)}

L {e^{t} sin (π t)} : \frac{π}{( s - 1 ) ^{2} + π ^{2}}

= e^{3} - 1 \cdot \frac{π}{( s - 1 ) ^{2} + π ^{2}}

Refine

e^{3} - 1 \frac{π}{( s - 1 ) ^{2} + π ^{2}} : e^{3} - \frac{π}{( s - 1 ) ^{2} + π ^{2}}

= e^{3} - \frac{π}{( s - 1 ) ^{2} + π ^{2}}

y^{^{'}} = y^{2} - 4

\int_{1}^{R} x^{- \frac{8}{5}} d x

\int x^{0} d x

\frac{d}{d x} (cos (arctan (6 x)))

\frac{d}{d x} (x^{4} (7 - x^{2})^{3})

What is laplacetransform e^3e^t(-sin(pit)) ?
The answer to laplacetransform e^3e^t(-sin(pit)) is e^3-pi/((s-1)^2+pi^2)