LaplaceTransform[Power[e,-2t]Power[Sin[t],2],t,s] - Wolfram|Alpha

Uh oh! Wolfram|Alpha doesn't run without JavaScript.

Please enable JavaScript. If you don't know how, you can find instructionshere.Once you've done that, refresh this page to start using Wolfram|Alpha.

Input

ℒ_t[e^(-2 t) sin^2(t)](s)

Result

2/((s + 2) (s^2 + 4 s + 8))

Expanded form

2/(s^3 + 6 s^2 + 16 s + 16)

Partial fraction expansion

(-s - 2)/(2 (s^2 + 4 s + 8)) + 1/(2 (s + 2))

Alternate form

2/(s (s (s + 6) + 16) + 16)

2/((s + 2) (s (s + 4) + 8))

Roots

(no roots exist)

Series expansion at s=0

1/8 - s/8 + (5 s^2)/64 - (5 s^3)/128 + (9 s^4)/512 + O(s^5)
(Taylor series)

Big‐O notation »

Series expansion at s=∞

2/s^3 - 12/s^4 + 40/s^5 - 80/s^6 + O((1/s)^7)
(Laurent series)

Big‐O notation »

Derivative

d/ds(2/((s + 2) (s^2 + 4 s + 8))) = -(2 (3 s^2 + 12 s + 16))/((s + 2)^2 (s^2 + 4 s + 8)^2)

Indefinite integral

integral2/((2 + s) (8 + 4 s + s^2)) ds = 1/2 log(s + 2) - 1/4 log(s^2 + 4 s + 8) + constant
(assuming a complex-valued logarithm)

Limit

lim_(s-> ± ∞) 2/((2 + s) (8 + 4 s + s^2)) = 0

POWERED BY THE WOLFRAM LANGUAGE