What is laplacetransform 5*e^{-3x}*sin(x)*x ?

The answer to laplacetransform 5*e^{-3x}*sin(x)*x is (5(2s+6))/((s^2+6s+10)^2)

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laplacetransform 5e^{-3x}sin(x)*x

laplace transform

5 \cdot e^{- 3 x} \cdot sin (x) \cdot x

\frac{5 ( 2 s + 6 )}{( s ^{2} + 6 s + 10 ) ^{2}}

Solution steps

L {5 e^{- 3 x} x sin (x)}

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)}

= 5 L {e^{- 3 x} sin (x) x}

L {e^{- 3 x} sin (x) x} : \frac{2 s + 6}{( s ^{2} + 6 s + 10 ) ^{2}}

= 5 \cdot \frac{2 s + 6}{( s ^{2} + 6 s + 10 ) ^{2}}

Refine

5 \frac{2 s + 6}{( s ^{2} + 6 s + 10 ) ^{2}} : \frac{5 ( 2 s + 6 )}{( s ^{2} + 6 s + 10 ) ^{2}}

= \frac{5 ( 2 s + 6 )}{( s ^{2} + 6 s + 10 ) ^{2}}

\frac{\partial}{\partial x} (ln (x - 6 y) - z)

\frac{d}{d x} (\frac{e ^{2 x}}{x ^{3}})

\int \frac{1}{x ( ln ( x ^{2} ) ) ^{4}} d x

x \to 0 - lim (\frac{- ln ( 1 + 6 x )}{x})

\int 2 x (x^{2} + 7)^{6} d x

What is laplacetransform 5*e^{-3x}*sin(x)*x ?
The answer to laplacetransform 5*e^{-3x}*sin(x)*x is (5(2s+6))/((s^2+6s+10)^2)