What is laplacetransform e^{3(t+1)} ?

The answer to laplacetransform e^{3(t+1)} is (e^3)/(s-3)

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laplacetransform e^{3(t+1)}

laplace transform

e^{3 (t + 1)}

\frac{e ^{3}}{s - 3}

Solution steps

L {e^{3 (t + 1)}}

Expand

e^{3 (t + 1)} : e^{3 t + 3}

= L {e^{3 t + 3}}

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} L {e^{3 t}}

L {e^{3 t}} : \frac{1}{s - 3}

= e^{3} \frac{1}{s - 3}

Refine

e^{3} \frac{1}{s - 3} : \frac{e ^{3}}{s - 3}

= \frac{e ^{3}}{s - 3}

y = x (3 x - 2)^{4}

\int x^{2} (4 + x^{3}) d x

x y^{^{'}} + y = 5 x y^{2}

\int \frac{1}{( 6 - x ^{2} ) ^{\frac{3}{2}}} d x

What is laplacetransform e^{3(t+1)} ?
The answer to laplacetransform e^{3(t+1)} is (e^3)/(s-3)