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人気のある微分積分 >

laplacetransform (t^2e^{-2t})/2

解

ラプラス変換

\frac{t ^{2} e ^{- 2 t}}{2}

解

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

解答ステップ

L {\frac{e ^{- 2 t} t ^{2}}{2}}

変換ルールを適用:

L {f (t)} = F (s)

ならば

L {e^{a t} f (t)} = F (s - a)

\frac{t ^{2} e ^{- 2 t}}{2}

向け

: f (t) = \frac{t ^{2}}{2}, a = - 2

= L {\frac{t ^{2}}{2}} (s + 2)

L {\frac{t ^{2}}{2}} : \frac{1}{s ^{3}}

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

人気の例

integral of 1/(u^2-3)

\int \frac{1}{u ^{2} - 3} d u

derivative of (x+8/3)

\frac{d}{d x} (\frac{x + 8}{3})

limit as x approaches 4 of 1/((x-4)^3)

x \to 4 lim (\frac{1}{( x - 4 ) ^{3}})

integral of 2xsec(x)tan(x)

\int 2 x sec (x) tan (x) d x

derivative of sqrt(4sin^2(x+9cos^2(x)))

\frac{d}{d x} (4 sin^{2} (x) + 9 cos^{2} (x))