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Popular >

laplacetransform 3e^{-2t}cos(t)

Solution

laplace transform

3 e^{- 2 t} cos (t)

Solution

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

Solution steps

L {3 e^{- 2 t} cos (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)}

= 3 L {e^{- 2 t} cos (t)}

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

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

Refine

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

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

Popular Examples

derivative of sqrt(t^2+1)derivative of

t^{2} + 1

derivative of 5+3sqrt(x)

\frac{d}{d x} (5 + 3 x)

integral of (5x-3)/(x^2+4)

\int \frac{5 x - 3}{x ^{2} + 4} d x

integral of 1/(x^2+4x+13)

\int \frac{1}{x ^{2} + 4 x + 13} d x

limit as x approaches pi of ln|cos(x)-7|

x \to π lim (ln ∣ cos (x) - 7 ∣)

Frequently Asked Questions (FAQ)

What is laplacetransform 3e^{-2t}cos(t) ?
The answer to laplacetransform 3e^{-2t}cos(t) is (3(s+2))/((s+2)^2+1)