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

The answer to laplacetransform 5*e^{-3x}*sin(5x)*x is (25(2s+6))/((s^2+6s+34)^2)

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

laplace transform

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

\frac{25 ( 2 s + 6 )}{( s ^{2} + 6 s + 34 ) ^{2}}

Solution steps

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

L {e^{- 3 x} sin (5 x) x} : \frac{5 ( 2 s + 6 )}{( s ^{2} + 6 s + 34 ) ^{2}}

= 5 \cdot \frac{5 ( 2 s + 6 )}{( s ^{2} + 6 s + 34 ) ^{2}}

Refine

5 \frac{5 ( 2 s + 6 )}{( s ^{2} + 6 s + 34 ) ^{2}} : \frac{25 ( 2 s + 6 )}{( s ^{2} + 6 s + 34 ) ^{2}}

= \frac{25 ( 2 s + 6 )}{( s ^{2} + 6 s + 34 ) ^{2}}

x \to 3 lim (5 - x)

\frac{1}{16} tan^{2} (x) + cos (x)

x \to 1 + lim (3 x)

\int \frac{x ^{2} + 10 x - 1}{x ^{3} - x} d x

What is laplacetransform 5*e^{-3x}*sin(5x)*x ?
The answer to laplacetransform 5*e^{-3x}*sin(5x)*x is (25(2s+6))/((s^2+6s+34)^2)