inverselaplace 3/((s+2)^3)

解答

的拉普拉斯逆变换

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

\frac{3 e ^{- 2 t} t ^{2}}{2}

求解步骤

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

应用逆变换法则: if

L^{- 1} {F (s)} = f (t)

则

L^{- 1} {F (s - a)} = e^{a t} f (t)

对于

\frac{3}{( s + 2 ) ^{3}} : a = - 2, F (s) = \frac{3}{s ^{3}}

= e^{- 2 t} L^{- 1} {\frac{3}{s ^{3}}}

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

= \frac{3 e ^{- 2 t} t ^{2}}{2}

a re a y = x^{3} - 2 x^{2} + 2, y = 3 x^{2} + 5 x - 23, - 1, 7

\frac{\partial}{\partial x} (x^{2} e^{- \frac{x}{y}})

\int_{1}^{5} \frac{e ^{\frac{x}{2}}}{x ^{3}} d x

a re a 3 e^{x}, 3 x e^{x^{2}}, [0, 1]

x \to 6 lim (2 x - 7)